subject:(singular integrals)

Oregon State University

1. Wang, Xi. On a class of singular integrals.

Degree: MS, Mathematics, 1989, Oregon State University

URL: http://hdl.handle.net/1957/40923

Subjects/Keywords: Singular integrals

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APA (6^th Edition):

Wang, X. (1989). On a class of singular integrals. (Masters Thesis). Oregon State University. Retrieved from http://hdl.handle.net/1957/40923

Chicago Manual of Style (16^th Edition):

Wang, Xi. “On a class of singular integrals.” 1989. Masters Thesis, Oregon State University. Accessed April 12, 2021. http://hdl.handle.net/1957/40923.

MLA Handbook (7^th Edition):

Wang, Xi. “On a class of singular integrals.” 1989. Web. 12 Apr 2021.

Vancouver:

Wang X. On a class of singular integrals. [Internet] [Masters thesis]. Oregon State University; 1989. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/1957/40923.

Council of Science Editors:

Wang X. On a class of singular integrals. [Masters Thesis]. Oregon State University; 1989. Available from: http://hdl.handle.net/1957/40923

Oregon State University

2. Glantz, Wayne L. A singular integral operator along a hypersurface.

Degree: PhD, Mathematics, 2001, Oregon State University

URL: http://hdl.handle.net/1957/16687

Subjects/Keywords: Singular integrals

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Glantz, W. L. (2001). A singular integral operator along a hypersurface. (Doctoral Dissertation). Oregon State University. Retrieved from http://hdl.handle.net/1957/16687

Chicago Manual of Style (16^th Edition):

Glantz, Wayne L. “A singular integral operator along a hypersurface.” 2001. Doctoral Dissertation, Oregon State University. Accessed April 12, 2021. http://hdl.handle.net/1957/16687.

MLA Handbook (7^th Edition):

Glantz, Wayne L. “A singular integral operator along a hypersurface.” 2001. Web. 12 Apr 2021.

Vancouver:

Glantz WL. A singular integral operator along a hypersurface. [Internet] [Doctoral dissertation]. Oregon State University; 2001. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/1957/16687.

Council of Science Editors:

Glantz WL. A singular integral operator along a hypersurface. [Doctoral Dissertation]. Oregon State University; 2001. Available from: http://hdl.handle.net/1957/16687

Macquarie University

3. Bui, The Anh. Singular integrals and function spaces.

Degree: 2012, Macquarie University

URL: http://hdl.handle.net/1959.14/229985

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Bibliography: pages 133-140.

1. Introduction – 2. Preliminaries – 3. Boundedness of some singular integrals with non-smooth kernels – 4. Hardy spaces associated to the… (more)

Subjects/Keywords: Singular integrals; Schrödinger operator; Hardy spaces; singular integral; hardy space

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bui, T. A. (2012). Singular integrals and function spaces. (Doctoral Dissertation). Macquarie University. Retrieved from http://hdl.handle.net/1959.14/229985

Chicago Manual of Style (16^th Edition):

Bui, The Anh. “Singular integrals and function spaces.” 2012. Doctoral Dissertation, Macquarie University. Accessed April 12, 2021. http://hdl.handle.net/1959.14/229985.

MLA Handbook (7^th Edition):

Bui, The Anh. “Singular integrals and function spaces.” 2012. Web. 12 Apr 2021.

Vancouver:

Bui TA. Singular integrals and function spaces. [Internet] [Doctoral dissertation]. Macquarie University; 2012. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/1959.14/229985.

Council of Science Editors:

Bui TA. Singular integrals and function spaces. [Doctoral Dissertation]. Macquarie University; 2012. Available from: http://hdl.handle.net/1959.14/229985

4. Taskinen, Matti. On the Implementation and Formulation of the Electromagnetic Surface Integral Equations.

Degree: 2006, Helsinki University of Technology

URL: http://lib.tkk.fi/Diss/2006/isbn9512281236/

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Surface integral equation method is one of the most popular numerical methods in the computational electromagnetics. In this thesis three problem areas in the implementation… (more)

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Surface integral equation method is one of the most popular numerical methods in the computational electromagnetics. In this thesis three problem areas in the implementation and formulation of the frequency domain surface integral equation methods are studied. First, a recursive technique is developed to evaluate the singular integrals arising from the electromagnetic surface integral equation methods. The technique is based on singularity subtraction method in which the most singular terms are extracted and evaluated analytically. A similar recursive algorithm is also developed for higher order basis functions. The technique is efficient and easy to apply for different surface integral equation formulations and polynomial basis functions. The second problem is how to model the electromagnetic fields in complex structures. A procedure is developed for this junction problem to model the fields separately in each region and to properly enforce the electromagnetic boundary conditions on the interfaces of the regions. The developed method is very simple and independent of the surface integral equation formulation and thus makes it easy to apply to different formulations. The third and most important problem is the choice of the electromagnetic surface integral equation formulation. Various traditional type of formulations are developed in this thesis and their behavior is studied especially with respect to the iterative methods. The most significant part of this thesis is the new type of a surface integral equation formulation and new techniques developed for it. The main idea in this new formulation is to use the surface charge densities as unknowns in addition to the traditional surface current densities. The formulation does not have problems with the low frequencies, it is well-balanced and the convergence of the iterative methods is fast for a very wide frequency range. The new formulation seems to be the first well-conditioned, truly broadband formulation that can be used from static to high frequencies in a general case of composite metallic and dielectric structures. The relation between the new formulation and the Picard's extended Maxwell system is also studied.

Electromagnetics Laboratory report series, ISSN 1456-632X; 470

Advisors/Committee Members: Helsinki University of Technology, Department of Electrical and Communications Engineering, Electromagnetics Laboratory.

Subjects/Keywords: electromagnetic surface integral equations; singular integrals; low frequency problem

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Taskinen, M. (2006). On the Implementation and Formulation of the Electromagnetic Surface Integral Equations. (Thesis). Helsinki University of Technology. Retrieved from http://lib.tkk.fi/Diss/2006/isbn9512281236/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Taskinen, Matti. “On the Implementation and Formulation of the Electromagnetic Surface Integral Equations.” 2006. Thesis, Helsinki University of Technology. Accessed April 12, 2021. http://lib.tkk.fi/Diss/2006/isbn9512281236/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Taskinen, Matti. “On the Implementation and Formulation of the Electromagnetic Surface Integral Equations.” 2006. Web. 12 Apr 2021.

Vancouver:

Taskinen M. On the Implementation and Formulation of the Electromagnetic Surface Integral Equations. [Internet] [Thesis]. Helsinki University of Technology; 2006. [cited 2021 Apr 12]. Available from: http://lib.tkk.fi/Diss/2006/isbn9512281236/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Taskinen M. On the Implementation and Formulation of the Electromagnetic Surface Integral Equations. [Thesis]. Helsinki University of Technology; 2006. Available from: http://lib.tkk.fi/Diss/2006/isbn9512281236/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Cornell University

5. Jung, Joeun. Iterated Trilinear Fourier Integrals With Arbitrary Symbols.

Degree: PhD, Mathematics, 2015, Cornell University

URL: http://hdl.handle.net/1813/40946

► My research interests fall under the broad categories of harmonic analysis and partial differential equations, with a particular focus on multilinear harmonic analysis with time-frequency… (more)

Subjects/Keywords: multilinear singular operators; time-frequency analysis; trilinear Fourier integrals

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Jung, J. (2015). Iterated Trilinear Fourier Integrals With Arbitrary Symbols. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/40946

Chicago Manual of Style (16^th Edition):

Jung, Joeun. “Iterated Trilinear Fourier Integrals With Arbitrary Symbols.” 2015. Doctoral Dissertation, Cornell University. Accessed April 12, 2021. http://hdl.handle.net/1813/40946.

MLA Handbook (7^th Edition):

Jung, Joeun. “Iterated Trilinear Fourier Integrals With Arbitrary Symbols.” 2015. Web. 12 Apr 2021.

Vancouver:

Jung J. Iterated Trilinear Fourier Integrals With Arbitrary Symbols. [Internet] [Doctoral dissertation]. Cornell University; 2015. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/1813/40946.

Council of Science Editors:

Jung J. Iterated Trilinear Fourier Integrals With Arbitrary Symbols. [Doctoral Dissertation]. Cornell University; 2015. Available from: http://hdl.handle.net/1813/40946

6. Cadilhac, Léonard. Weak type inequalities in noncommutative Lp-spaces : Inégalités de type faible dans les espaces Lp non-commutatifs.

Degree: Docteur es, Mathématiques, 2019, Normandie

URL: http://www.theses.fr/2019NORMC213

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Cette thèse vise à développer des outils d'analyse harmonique non-commutative. Elle porte plus précisément sur les inégalités de Khintchine non-commutatives et les intégrales singulières à… (more)

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Cette thèse vise à développer des outils d'analyse harmonique non-commutative. Elle porte plus précisément sur les inégalités de Khintchine non-commutatives et les intégrales singulières à valeurs opérateur. La première partie est dédiée à des questions d'interpolation des espaces Lp classiques. On généralise et on énonce de nouvelles caractérisations des espaces interpolés entre espaces Lp. Dans une seconde partie, on démontre une forme des inégalités de Khintchine non-commutatives valides dans tous les espaces interpolés entre espace Lp. Celle-ci permet d’unifier les cas p < 2 et p > 2 ainsi que de traiter les espaces Lp faibles, même pour p = 1 ou 2. En s'appuyant sur la première partie, on caractérise les espaces dans lesquels les formules usuelles pour les inégalités de Khintchine sont valides. Dans une dernière partie, on donne une preuve simplifiée de l'inégalité de type (1,1) faible pour les intégrales singulières non-commutatives, un résultat précédemment obtenu par Parcet. Cette simplification nous permet de retrouver rapidement deux autres résultats connus : la pseudolocalisation Lp et l’inégalité de type faible pour les intégrales singulières non-commutatives dont le noyau est à valeurs dans un espace de Hilbert.

The purpose of this thesis is to develop tools of noncommutative harmonic analysis. More precisely, it deals with noncommutative Khintchine inequalities and operator-valued singular integrals. The first part is dedicated to questions of interpolation between classical Lp-spaces. We generalize and state new characterisations of interpolation spaces between Lp-spaces. In a second part, we introduce a form of the noncommutative Khintchine inequalities which holds in every interpolation space between two Lp-spaces. It enables us to unify the cases p < 2 and p > 2 and to deal with weak Lp-spaces even when p = 1 or 2. By relying on the first part, we characterize spaces in which the usual formulas for Khintchine inequalities hold. In a last part, we give a simplified proof of the weak boundedness of noncommutative singular integrals, a result previously obtained by Parcet. This simplification allows us to recover quickly two results: the Lp pseudolocalisation and the weak type inequality for noncommutative singular integrals associated to Hilbert-valued kernels.

Advisors/Committee Members: Ricard, Eric (thesis director).

Subjects/Keywords: Inégalités de Khintchine non-commutatives; Noncommutative Khintchine inequalities; Singular integrals

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Cadilhac, L. (2019). Weak type inequalities in noncommutative Lp-spaces : Inégalités de type faible dans les espaces Lp non-commutatifs. (Doctoral Dissertation). Normandie. Retrieved from http://www.theses.fr/2019NORMC213

Chicago Manual of Style (16^th Edition):

Cadilhac, Léonard. “Weak type inequalities in noncommutative Lp-spaces : Inégalités de type faible dans les espaces Lp non-commutatifs.” 2019. Doctoral Dissertation, Normandie. Accessed April 12, 2021. http://www.theses.fr/2019NORMC213.

MLA Handbook (7^th Edition):

Cadilhac, Léonard. “Weak type inequalities in noncommutative Lp-spaces : Inégalités de type faible dans les espaces Lp non-commutatifs.” 2019. Web. 12 Apr 2021.

Vancouver:

Cadilhac L. Weak type inequalities in noncommutative Lp-spaces : Inégalités de type faible dans les espaces Lp non-commutatifs. [Internet] [Doctoral dissertation]. Normandie; 2019. [cited 2021 Apr 12]. Available from: http://www.theses.fr/2019NORMC213.

Council of Science Editors:

Cadilhac L. Weak type inequalities in noncommutative Lp-spaces : Inégalités de type faible dans les espaces Lp non-commutatifs. [Doctoral Dissertation]. Normandie; 2019. Available from: http://www.theses.fr/2019NORMC213

Tartu University

7. Orav-Puurand, Kerli. Central Part Interpolation Schemes for Weakly Singular Integral Equations .

Degree: 2014, Tartu University

URL: http://hdl.handle.net/10062/44269

► Paljud keemia, polümeeride füüsika, matemaatilise füüsika jt teadusalade probleemid on formuleeritavad integraalvõrrandite kujul ning nende probleemide käsitlus taandub integraalvõrrandite lahendamisele või kvalitatiivsele uurimisele. Integraalvõrrandeid, mida… (more)

▼ Paljud keemia, polümeeride füüsika, matemaatilise füüsika jt teadusalade probleemid on formuleeritavad integraalvõrrandite kujul ning nende probleemide käsitlus taandub integraalvõrrandite lahendamisele või kvalitatiivsele uurimisele. Integraalvõrrandeid, mida saab täpselt lahendada, on suhteliselt vähe, seega on väga olulised meetodid võrrandite numbriliseks lahendamiseks. Käesolevas doktoritöös pakume välja kaks kõrget järku numbrilist meetodit, mis ei kasuta lineaarse teist liiki singulaarsustega Fredholmi integraalvõrrandi lahendamiseks ebaühtlast võrku. Need meetodid on kollokatsioonimeetod ja korrutise integreerimise meetod. Nimetatud meetodid põhinevad keskosa interpolatsioonil polünoomidega ühtlasel võrgul ja silendaval muutujate vahetusel. Lõigu keskosas on interpolatsioonivea hinnang ligikaudu 2m korda täpsem kui kogu lõigul. Lisaks on interpolatsiooniprotsess ühtlasel võrgul lõigu keskosas m-i kasvades stabiilne. Muutujate vahetuse abil parendame me võrrandi täpse lahendi käitumist. Doktoritöös on kirjeldatud toodud meetodite koondumist ja koondumiskiirust; There are a number of problems from many different fields, for example chemistry, physics of polymers and mathematical physics, which are directly formulated in terms of integral equations; and there are problems that are represented in terms of differential equations with auxiliary conditions, but which can be reduced to integral equations. There are relatively few integral equations which can be solved exactly, hence, numerical schemes are required for dealing with these equations in a proper manner. In this thesis we propose two new classes of high order numerical methods, which do not need graded grids for solving linear Fredholm integral equations of the second kind with singularities. The methods are developed by means of the 'central part' interpolation by polynomials on the uniform grid and smoothing change of variables. In the central parts of the interval, the estimates of interpolation error are approximately 2m times more precise than on the whole interval. In the central parts of the interval, the interpolation process on the uniform grid also has good stability properties as m increases. With the help of a change of variables we improve the boundary behaviour of the exact solution of the problem. The convergence and the convergence order of methods is studied.

Subjects/Keywords: singulaarsed integraalid; integraalvõrrandid; interpoleerimine; singular integrals; integral equations; interpolation

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APA (6^th Edition):

Orav-Puurand, K. (2014). Central Part Interpolation Schemes for Weakly Singular Integral Equations . (Thesis). Tartu University. Retrieved from http://hdl.handle.net/10062/44269

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Orav-Puurand, Kerli. “Central Part Interpolation Schemes for Weakly Singular Integral Equations .” 2014. Thesis, Tartu University. Accessed April 12, 2021. http://hdl.handle.net/10062/44269.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Orav-Puurand, Kerli. “Central Part Interpolation Schemes for Weakly Singular Integral Equations .” 2014. Web. 12 Apr 2021.

Vancouver:

Orav-Puurand K. Central Part Interpolation Schemes for Weakly Singular Integral Equations . [Internet] [Thesis]. Tartu University; 2014. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/10062/44269.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Orav-Puurand K. Central Part Interpolation Schemes for Weakly Singular Integral Equations . [Thesis]. Tartu University; 2014. Available from: http://hdl.handle.net/10062/44269

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

8. Vitturi, Marco. Double Hilbert transforms along surfaces in the Heisenberg group.

Degree: PhD, 2017, University of Edinburgh

URL: http://hdl.handle.net/1842/25418

► We provide an L² theory for the local double Hilbert transform along an analytic surface (s, t ,φ(s, t )) in the Heisenberg group H¹,… (more)

Subjects/Keywords: 515; harmonic analysis; multi-parameter singular integrals; Heisenberg group

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APA (6^th Edition):

Vitturi, M. (2017). Double Hilbert transforms along surfaces in the Heisenberg group. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/25418

Chicago Manual of Style (16^th Edition):

Vitturi, Marco. “Double Hilbert transforms along surfaces in the Heisenberg group.” 2017. Doctoral Dissertation, University of Edinburgh. Accessed April 12, 2021. http://hdl.handle.net/1842/25418.

MLA Handbook (7^th Edition):

Vitturi, Marco. “Double Hilbert transforms along surfaces in the Heisenberg group.” 2017. Web. 12 Apr 2021.

Vancouver:

Vitturi M. Double Hilbert transforms along surfaces in the Heisenberg group. [Internet] [Doctoral dissertation]. University of Edinburgh; 2017. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/1842/25418.

Council of Science Editors:

Vitturi M. Double Hilbert transforms along surfaces in the Heisenberg group. [Doctoral Dissertation]. University of Edinburgh; 2017. Available from: http://hdl.handle.net/1842/25418

Macquarie University

9. Ly, Fu Ken. Riesz transforms, function spaces, and weighted estimates for Schrödinger operators with non-negative potentials.

Degree: PhD, 2012, Macquarie University

URL: http://hdl.handle.net/1959.14/228374

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Bibliography: pages 185-190.

1. Introduction – 2. Some preliminaries – 3. Heat kernel estimates – 4. Weighted Lebesgue spaces I: Muckenhoupt weights – 5. Weighted… (more)

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Bibliography: pages 185-190.

1. Introduction – 2. Some preliminaries – 3. Heat kernel estimates – 4. Weighted Lebesgue spaces I: Muckenhoupt weights – 5. Weighted Lebesgue spaces II: weights adapted to the Schrödinger operator – 6. Morrey spaces and Muckenhoupt weights – 7. Hardy spaces and Schrödinger operators – 8. A class of potentials beyond the reverse Hölder class.

The main aim of this thesis is to obtain estimates for Riesz transforms associated to the Schrödinger operator with non-negative potentials on various function spaces over the Euclidean spaces. Our results concern the first- and second-order Riesz transforms on the weighted Lp spaces, the Hardy spaces, and the Morrey spaces. We describe our main results briefly in the following. – We show that the Lp boundedness of the first-order Riesz transforms within a range of exponents is equivalent, firstly to their boundedness on the weighted Lp spaces within a specific range of both p and (Muckenhoupt) weights, and secondly to their boundedness on the Morrey spaces Lp,λ within a specific range of parameters p and λ. – On specialising to the case where the potential satisfies a reverse Hölder inequality up to some exponent, we show that the second-order Riesz transforms are bounded on three classes of function spaces: the weighted Lebesgue spaces, the Hardy spaces associated to the Schrödinger operator, and the Morrey spaces, again within a specific range of parameters; this time depending on the reverse Hölder exponent. This is achieved through some new estimates on the heat kernel (associated to the Schrödinger operator) that we derive within this context. These estimates involve the time and the spatial derivatives and have extra global decay over the usual Gaussian. – In this setting we also study a class of weights that generalise the Muckenhoupt weights and are adapted to the Schrödinger operator in a certain sense. We develop some new good-λ estimates that provide a systematic framework for investigating operators lacking kernel regularity on Lp spaces with these weights.

1 online resource (xii, 190 pages)

Advisors/Committee Members: Macquarie University. Department of Mathematics.

Subjects/Keywords: Harmonic analysis; Singular integrals; riesz transforms; Schrödinger operators

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ly, F. K. (2012). Riesz transforms, function spaces, and weighted estimates for Schrödinger operators with non-negative potentials. (Doctoral Dissertation). Macquarie University. Retrieved from http://hdl.handle.net/1959.14/228374

Chicago Manual of Style (16^th Edition):

Ly, Fu Ken. “Riesz transforms, function spaces, and weighted estimates for Schrödinger operators with non-negative potentials.” 2012. Doctoral Dissertation, Macquarie University. Accessed April 12, 2021. http://hdl.handle.net/1959.14/228374.

MLA Handbook (7^th Edition):

Ly, Fu Ken. “Riesz transforms, function spaces, and weighted estimates for Schrödinger operators with non-negative potentials.” 2012. Web. 12 Apr 2021.

Vancouver:

Ly FK. Riesz transforms, function spaces, and weighted estimates for Schrödinger operators with non-negative potentials. [Internet] [Doctoral dissertation]. Macquarie University; 2012. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/1959.14/228374.

Council of Science Editors:

Ly FK. Riesz transforms, function spaces, and weighted estimates for Schrödinger operators with non-negative potentials. [Doctoral Dissertation]. Macquarie University; 2012. Available from: http://hdl.handle.net/1959.14/228374

Purdue University

10. Perlmutter, Michael A. Martingales, Singular Integrals, and Fourier Multipliers.

Degree: PhD, Mathematics, 2016, Purdue University

URL: https://docs.lib.purdue.edu/open_access_dissertations/829

► Many probabilistic constructions have been created to study the Lp-boundedness, 1 < p < ∞, of singular integrals and Fourier multipliers. We will use… (more)

Subjects/Keywords: Pure sciences; Beurling-ahlfors; Harmonic analysis; Martingales; Probability; Singular integrals; Mathematics

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APA (6^th Edition):

Perlmutter, M. A. (2016). Martingales, Singular Integrals, and Fourier Multipliers. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/829

Chicago Manual of Style (16^th Edition):

Perlmutter, Michael A. “Martingales, Singular Integrals, and Fourier Multipliers.” 2016. Doctoral Dissertation, Purdue University. Accessed April 12, 2021. https://docs.lib.purdue.edu/open_access_dissertations/829.

MLA Handbook (7^th Edition):

Perlmutter, Michael A. “Martingales, Singular Integrals, and Fourier Multipliers.” 2016. Web. 12 Apr 2021.

Vancouver:

Perlmutter MA. Martingales, Singular Integrals, and Fourier Multipliers. [Internet] [Doctoral dissertation]. Purdue University; 2016. [cited 2021 Apr 12]. Available from: https://docs.lib.purdue.edu/open_access_dissertations/829.

Council of Science Editors:

Perlmutter MA. Martingales, Singular Integrals, and Fourier Multipliers. [Doctoral Dissertation]. Purdue University; 2016. Available from: https://docs.lib.purdue.edu/open_access_dissertations/829

Michigan State University

11. Rey, Guillermo. Sharp estimates in harmonic analysis.

Degree: 2015, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:3556

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Thesis Ph. D. Michigan State University. Mathematics 2015.

We investigate certain sharp estimates related to singular integrals. In particular we give sharp level set estimates… (more)

Subjects/Keywords: Harmonic analysis – Mathematical models; Singular integrals – Mathematical models; Mathematics

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APA (6^th Edition):

Rey, G. (2015). Sharp estimates in harmonic analysis. (Thesis). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:3556

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Rey, Guillermo. “Sharp estimates in harmonic analysis.” 2015. Thesis, Michigan State University. Accessed April 12, 2021. http://etd.lib.msu.edu/islandora/object/etd:3556.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Rey, Guillermo. “Sharp estimates in harmonic analysis.” 2015. Web. 12 Apr 2021.

Vancouver:

Rey G. Sharp estimates in harmonic analysis. [Internet] [Thesis]. Michigan State University; 2015. [cited 2021 Apr 12]. Available from: http://etd.lib.msu.edu/islandora/object/etd:3556.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Rey G. Sharp estimates in harmonic analysis. [Thesis]. Michigan State University; 2015. Available from: http://etd.lib.msu.edu/islandora/object/etd:3556

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Universitat Autònoma de Barcelona

12. Puliatti, Carmelo. Singular integrals, rectifiability and elliptic measure.

Degree: Departament de Matemàtiques, 2019, Universitat Autònoma de Barcelona

URL: http://hdl.handle.net/10803/670127

► The thesis investigates the relation between the geometric properties of measures in Euclidean spaces and the behavior of certain associated singular integral operators. We also… (more)

▼ The thesis investigates the relation between the geometric properties of measures in Euclidean spaces and the behavior of certain associated singular integral operators. We also show some application to the study of elliptic PDEs. First, we characterize the regularity of the planar chord-arc Jordan curves whose associated maximal Cauchy transform can be pointwise dominated by the second-order iteration of the Hardy-Littlewood maximal function on the curve, assuming a natural background asymptotic conformality condition. In particular, it turns out that this curves do not necessarily have tangents at each point but they are differentiable almost everywhere with derivatives in VMO. The conditions on a measure that determine whether its associated Cauchy transform defines a compact operator on L² are studied in the second chapter; we determine that the compactness can be characterized by a uniform convergence to zero of the upper density of the measure. Then, we investigate an equivalent in the context of elliptic equations of two important recent results on Riesz transform and uniform rectifiabilty. Under a Hölder continuity assumption for the matrix defining the uniformly elliptic operator in divergence form we prove, in collaboration with Laura Prat and Xavier Tolsa, that the gradient of the single layer potential associated with a compactly supported n-Alhfors-David regular mesaure in R^(n+1) is bounded on L² if and only if the measure is uniformly n-rectifiable. This result extends the important article by F. Nazarov, X. Tolsa and A. Volberg on the solution of the so-called co-dimension 1 David and Semmes’ problem and we apply it to a one-phase problem for the elliptic measure. Under the same hypothesis for the elliptic equation we establish a local rectifiability criterion for Radon measures which are not necessarily regular. The theorem is formulated in terms of a control of the mean oscillation of the gradient of the single layer potential. This generalizes a recent result by D. Girela-Sarriòn and X. Tolsa. This study constitutes an important step to achieve a rectifiability result for a two-phase problem for the elliptic measure. Advisors/Committee Members: [email protected] (authoremail), true (authoremailshow), Tolsa Domènech, Xavier (director), Verdera, Joan (director).

Subjects/Keywords: Integrals singulars; Integrales singulares; Singular integrals; Rectificabilitat; Rectificabilidad; Rectifiability; Mesura el·líptica; Medida elíptica; Elliptic measure; Ciències Experimentals; 517

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APA (6^th Edition):

Puliatti, C. (2019). Singular integrals, rectifiability and elliptic measure. (Thesis). Universitat Autònoma de Barcelona. Retrieved from http://hdl.handle.net/10803/670127

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Puliatti, Carmelo. “Singular integrals, rectifiability and elliptic measure.” 2019. Thesis, Universitat Autònoma de Barcelona. Accessed April 12, 2021. http://hdl.handle.net/10803/670127.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Puliatti, Carmelo. “Singular integrals, rectifiability and elliptic measure.” 2019. Web. 12 Apr 2021.

Vancouver:

Puliatti C. Singular integrals, rectifiability and elliptic measure. [Internet] [Thesis]. Universitat Autònoma de Barcelona; 2019. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/10803/670127.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Puliatti C. Singular integrals, rectifiability and elliptic measure. [Thesis]. Universitat Autònoma de Barcelona; 2019. Available from: http://hdl.handle.net/10803/670127

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of New Mexico

13. Atasever, Nuriye. The Hilbert Transform as an Average of Dyadic Shift Operators.

Degree: Mathematics & Statistics, 2015, University of New Mexico

URL: http://hdl.handle.net/1928/25730

► In this thesis we discuss Petermichls characterization of the Hilbert transform as an average of dyadic shift operators following the presentation by Thomas Hytonen [Hyt].… (more)

Subjects/Keywords: Hilbert Transform; Dyadic Shift Operators; Random Dyadic Grids; Singular Integrals; Fourier Multipliers

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APA (6^th Edition):

Atasever, N. (2015). The Hilbert Transform as an Average of Dyadic Shift Operators. (Masters Thesis). University of New Mexico. Retrieved from http://hdl.handle.net/1928/25730

Chicago Manual of Style (16^th Edition):

Atasever, Nuriye. “The Hilbert Transform as an Average of Dyadic Shift Operators.” 2015. Masters Thesis, University of New Mexico. Accessed April 12, 2021. http://hdl.handle.net/1928/25730.

MLA Handbook (7^th Edition):

Atasever, Nuriye. “The Hilbert Transform as an Average of Dyadic Shift Operators.” 2015. Web. 12 Apr 2021.

Vancouver:

Atasever N. The Hilbert Transform as an Average of Dyadic Shift Operators. [Internet] [Masters thesis]. University of New Mexico; 2015. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/1928/25730.

Council of Science Editors:

Atasever N. The Hilbert Transform as an Average of Dyadic Shift Operators. [Masters Thesis]. University of New Mexico; 2015. Available from: http://hdl.handle.net/1928/25730

University of Kansas

14. Chaffee, Lucas. Commutators of Multilinear Singular Integral Operators with Pointwise Multiplication.

Degree: PhD, Mathematics, 2015, University of Kansas

URL: http://hdl.handle.net/1808/19020

► In this dissertation we further develop the theory of commutators of multilinear singular integral operators with pointwise multiplication. Generally speaking, the commutator of two operators… (more)

Subjects/Keywords: Mathematics; BMO; Calderon Zygmund Theory; Commutators; Harmonic Analysis; Multilinear Operators; Singular integrals

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APA (6^th Edition):

Chaffee, L. (2015). Commutators of Multilinear Singular Integral Operators with Pointwise Multiplication. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/19020

Chicago Manual of Style (16^th Edition):

Chaffee, Lucas. “Commutators of Multilinear Singular Integral Operators with Pointwise Multiplication.” 2015. Doctoral Dissertation, University of Kansas. Accessed April 12, 2021. http://hdl.handle.net/1808/19020.

MLA Handbook (7^th Edition):

Chaffee, Lucas. “Commutators of Multilinear Singular Integral Operators with Pointwise Multiplication.” 2015. Web. 12 Apr 2021.

Vancouver:

Chaffee L. Commutators of Multilinear Singular Integral Operators with Pointwise Multiplication. [Internet] [Doctoral dissertation]. University of Kansas; 2015. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/1808/19020.

Council of Science Editors:

Chaffee L. Commutators of Multilinear Singular Integral Operators with Pointwise Multiplication. [Doctoral Dissertation]. University of Kansas; 2015. Available from: http://hdl.handle.net/1808/19020

Macquarie University

15. Peate, Joshua Grahame. Riesz Transform estimates in the absence of a preservation condition and applications to the Dirichlet Laplacian.

Degree: 2015, Macquarie University

URL: http://hdl.handle.net/1959.14/1067171

►

Theoretical thesis.

Bibliography: pages 175-182.

I. Introduction and main results. 1. Introduction ; 2. Preliminaries ; 3. A Riesz Transform bound part 1: a general… (more)

▼

Theoretical thesis.

Bibliography: pages 175-182.

I. Introduction and main results. 1. Introduction ; 2. Preliminaries ; 3. A Riesz Transform bound part 1: a general result in the absence of a preservation condition ; 4. A Riesz Transform bound part 2: a non-doubling variation ; 5. A Riesz Transform bound part 3: a weighted result ; 6. Weighted maximal functions on domains – II. Applications to the Dirichlet Laplacian. 7. Heat kernel bounds ; 8. Heat semigroup and related bounds ; 9. Weighted hardy estimates ; 10 Riesz Transform for the Dirichlet Laplacian.

R. Strichartz in [68] asked whether the Lp boundedness of the Riesz transform observed on Rn could be extended to a reasonable class of non-compact manifolds. Many partial answers have been given since. One such answer given by Auscher, Coulhon, Duong and Hofmann in [5] tied the Lp boundedness of the Riesz transform to the Lp boundedness of the Gaffney inequality. Their result was for p > 2 and held on noncompact manifolds satisfying doubling and Poincaré conditions, along with a stochastic completeness or preservation condition. In this thesis the results of [5] are adapted to prove Lp bounds, p > 2, for Riesz transform variations in cases where a preservation condition does not hold. To compensate for the lack of a preservation condition, two new conditions are required. The results are general enough to apply in a large number of circumstances. Two extensions on this result are additionally presented. The first extension is to non-doubling domains. This extension is specifically in the circumstance of a manifold with boundary and Dirichlet boundary conditions. An added benefit of this non-doubling extension is that the Poincaré inequality is no longer required near the boundary. The second extension shows that the weighted Lp boundedness of the Riesz transform observed on Rn can also be extended in some degree to a reasonable class of non-compact manifolds. This second extension includes generalised deriving of weight classes associated to skewed maximal functions and other operators. This thesis also contains applications to the case of the Dirichlet Laplacian on various subsets of Rn. The overall work and particularly the application are motivated by recent results from Killip, Visan and Zhang in [48].

1 online resource (ix, 182 pages)

Advisors/Committee Members: Macquarie University. Department of Mathematics.

Subjects/Keywords: Riesz spaces; Dirichlet forms; harmonic analysis; Riesz Transforms; singular integrals; heat kernels

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APA (6^th Edition):

Peate, J. G. (2015). Riesz Transform estimates in the absence of a preservation condition and applications to the Dirichlet Laplacian. (Doctoral Dissertation). Macquarie University. Retrieved from http://hdl.handle.net/1959.14/1067171

Chicago Manual of Style (16^th Edition):

Peate, Joshua Grahame. “Riesz Transform estimates in the absence of a preservation condition and applications to the Dirichlet Laplacian.” 2015. Doctoral Dissertation, Macquarie University. Accessed April 12, 2021. http://hdl.handle.net/1959.14/1067171.

MLA Handbook (7^th Edition):

Peate, Joshua Grahame. “Riesz Transform estimates in the absence of a preservation condition and applications to the Dirichlet Laplacian.” 2015. Web. 12 Apr 2021.

Vancouver:

Peate JG. Riesz Transform estimates in the absence of a preservation condition and applications to the Dirichlet Laplacian. [Internet] [Doctoral dissertation]. Macquarie University; 2015. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/1959.14/1067171.

Council of Science Editors:

Peate JG. Riesz Transform estimates in the absence of a preservation condition and applications to the Dirichlet Laplacian. [Doctoral Dissertation]. Macquarie University; 2015. Available from: http://hdl.handle.net/1959.14/1067171

16. Ubessi, Cristiano João Brizzi. Método dos elementos de contorno para elasticidade linear 3D com avaliação direta das integrais singulares.

Degree: 2014, Brazil

URL: http://hdl.handle.net/10183/108490

►

Este trabalho apresenta a formulação e implementação numérica do método dos elementos de contorno (MEC) para elasticidade linear tri-dimensional, com avaliação direta das integrais fracamente… (more)

▼

Este trabalho apresenta a formulação e implementação numérica do método dos elementos de contorno (MEC) para elasticidade linear tri-dimensional, com avaliação direta das integrais fracamente e fortemente singulares. A implementação segue a formulação tradicional do MEC direto, e a discretização do contorno das variáveis do problema é realizada com elementos descontínuos, permitindo o uso de malhas desconectadas ao longo das superfícies. O cálculo das integrais singulares é realizado através do uso de expansões assintóticas calculadas em torno de um ponto singular genérico. As expressões analíticas destas expansões são apresentadas no trabalho. Estas expansões serão subtraídas do núcleo original regularizando-o e a parte singular é integrada analiticamente, restando apenas uma integral regular, tornando ambas as integrais possíveis de serem calculadas com quadraturas de Gauss. É concluído que o presente método requer menos pontos de integração para o mesmo nível de erro quando comparado com outras técnicas. Alguns casos de elasticidade são resolvidos para ilustrar a eficiência e precisão do método.

This work presents the formulation and implementation of the boundary element method (BEM) to three dimensional linear elastostatics, with the direct evaluation of the strongly singular integral equations. The implementation follows the traditional direct BEM formulation, and the discretization of the boundary is carried out with discontinuous elements, enabling the use of disconnected meshes along the surfaces. The computation of the singular integral equations is accomplished by using the asymptotic expansions derived around a generic singular point. The analytical expressions for these expansions are presented in this work. The expansions are subtracted from the kernel to regularize it. This subtracted part is then added by computing a regular line integral along the boundary of the element. Both the integrals can be calculated with Gauss-type quadratures. It's observed that the present method needs less integration points for the same level of error when compared with other techniques. Several elasticity benchmarks are solved to demonstrate the eficiency and the accuracy of the present method.

Advisors/Committee Members: Marczak, Rogerio Jose.

Subjects/Keywords: Elementos de contorno; Elasticidade; Equações integrais; Boundary element method; Regularization; Singular integrals; Tridimensional elasticity

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APA (6^th Edition):

Ubessi, C. J. B. (2014). Método dos elementos de contorno para elasticidade linear 3D com avaliação direta das integrais singulares. (Masters Thesis). Brazil. Retrieved from http://hdl.handle.net/10183/108490

Chicago Manual of Style (16^th Edition):

Ubessi, Cristiano João Brizzi. “Método dos elementos de contorno para elasticidade linear 3D com avaliação direta das integrais singulares.” 2014. Masters Thesis, Brazil. Accessed April 12, 2021. http://hdl.handle.net/10183/108490.

MLA Handbook (7^th Edition):

Ubessi, Cristiano João Brizzi. “Método dos elementos de contorno para elasticidade linear 3D com avaliação direta das integrais singulares.” 2014. Web. 12 Apr 2021.

Vancouver:

Ubessi CJB. Método dos elementos de contorno para elasticidade linear 3D com avaliação direta das integrais singulares. [Internet] [Masters thesis]. Brazil; 2014. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/10183/108490.

Council of Science Editors:

Ubessi CJB. Método dos elementos de contorno para elasticidade linear 3D com avaliação direta das integrais singulares. [Masters Thesis]. Brazil; 2014. Available from: http://hdl.handle.net/10183/108490

17. Roxana Bedoya Prado. Operadores de Calderón-Zygmund e o teorema T1.

Degree: 2009, Universidade Federal de São Carlos

URL: http://www.bdtd.ufscar.br/htdocs/tedeSimplificado//tde_busca/arquivo.php?codArquivo=2592

►

Neste trabalho, apresentamos condições necessárias e suficientes para que um operador de tipo Calderón-Zygmund possa ser estendido a um operador limitado em L2. Usando resultados… (more)

Subjects/Keywords: Análise harmônica; Integrais singulares; Fourier, Análise de; MATEMATICA; Harmonic analysis; Singular integrals; Calderón-Zygmund operators; The T1 theorem

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APA (6^th Edition):

Prado, R. B. (2009). Operadores de Calderón-Zygmund e o teorema T1. (Thesis). Universidade Federal de São Carlos. Retrieved from http://www.bdtd.ufscar.br/htdocs/tedeSimplificado//tde_busca/arquivo.php?codArquivo=2592

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Prado, Roxana Bedoya. “Operadores de Calderón-Zygmund e o teorema T1.” 2009. Thesis, Universidade Federal de São Carlos. Accessed April 12, 2021. http://www.bdtd.ufscar.br/htdocs/tedeSimplificado//tde_busca/arquivo.php?codArquivo=2592.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Prado, Roxana Bedoya. “Operadores de Calderón-Zygmund e o teorema T1.” 2009. Web. 12 Apr 2021.

Vancouver:

Prado RB. Operadores de Calderón-Zygmund e o teorema T1. [Internet] [Thesis]. Universidade Federal de São Carlos; 2009. [cited 2021 Apr 12]. Available from: http://www.bdtd.ufscar.br/htdocs/tedeSimplificado//tde_busca/arquivo.php?codArquivo=2592.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Prado RB. Operadores de Calderón-Zygmund e o teorema T1. [Thesis]. Universidade Federal de São Carlos; 2009. Available from: http://www.bdtd.ufscar.br/htdocs/tedeSimplificado//tde_busca/arquivo.php?codArquivo=2592

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Universitat Autònoma de Barcelona

18. Chunaev, Petr. Singular integral operators and rectifiability.

Degree: Departament de Matemàtiques, 2018, Universitat Autònoma de Barcelona

URL: http://hdl.handle.net/10803/663827

► The problems that we study in this thesis lie in the area of Harmonic Analysis and Geometric Measure Theory. Namely, we consider the connection between… (more)

Subjects/Keywords: Operadors integrals singulars; Operadores integrales singulares; Singular integral operator; Rectificabilitat; Rectificabilidad; Rectififiability; transformada de Cauchy; Cauchy transform; Ciències Experimentals; 51

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APA (6^th Edition):

Chunaev, P. (2018). Singular integral operators and rectifiability. (Thesis). Universitat Autònoma de Barcelona. Retrieved from http://hdl.handle.net/10803/663827

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chunaev, Petr. “Singular integral operators and rectifiability.” 2018. Thesis, Universitat Autònoma de Barcelona. Accessed April 12, 2021. http://hdl.handle.net/10803/663827.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chunaev, Petr. “Singular integral operators and rectifiability.” 2018. Web. 12 Apr 2021.

Vancouver:

Chunaev P. Singular integral operators and rectifiability. [Internet] [Thesis]. Universitat Autònoma de Barcelona; 2018. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/10803/663827.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chunaev P. Singular integral operators and rectifiability. [Thesis]. Universitat Autònoma de Barcelona; 2018. Available from: http://hdl.handle.net/10803/663827

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Duke University

19. Nicholas, Michael J. A Third Order Numerical Method for Doubly Periodic Electromegnetic Scattering .

Degree: 2007, Duke University

URL: http://hdl.handle.net/10161/383

► We here developed a third-order accurate numerical method for scattering of 3D electromagnetic waves by doubly periodic structures. The method is an intuitively simple numerical… (more)

▼ We here developed a third-order accurate numerical method for scattering of 3D electromagnetic waves by doubly periodic structures. The method is an intuitively simple numerical scheme based on a boundary integral formulation. It involves smoothing the singular Green's functions in the integrands and finding correction terms to the resulting smooth integrals. The analytical method is based on the singular integral methods of J. Thomas Beale, while the scattering problem is motivated by the 2D work of Stephanos Venakides, Mansoor Haider, and Stephen Shipman. The 3D problem was done with boundary element methods by Andrew Barnes. We present a method that is both more straightforward and more accurate. In solving these problems, we have used the Müller integral equation formulation of Maxwell's equations, since it is a Fredholm integral equation of the second kind and is well-posed. Müller derived his equations for the case of a compact scatterer. We outline the derivation and adapt it to a periodic scatterer. The periodic Green's functions found in the integral equation contain singularities which make it difficult to evaluate them numerically with accuracy. These functions are also very time consuming to evaluate numerically. We use Ewald splitting to represent these functions in a way that can be computed rapidly.We present a method of smoothing the singularity of the Green's function while maintaining its periodicity. We do local analysis of the singularity in order to identify and eliminate the largest sources of error introduced by this smoothing. We prove that with our derived correction terms, we can replace the singular integrals with smooth integrals and only introduce a error that is third order in the grid spacing size. The derivation of the correction terms involves transforming to principal directions using concepts from differential geometry. The correction terms are necessarily invariant under this transformation and depend on geometric properties of the scatterer such as the mean curvature and the differential of the Gauss map. Able to evaluate the integrals to a higher order, we implement a {GMRES} algorithm to approximate solutions of the integral equation. From these solutions, Müller's equations allow us to compute the scattered fields and transmission coefficients. We have also developed acceleration techniques that allow for more efficient computation.We provide results for various scatterers, including a test case for which exact solutions are known. The implemented method does indeed converge with third order accuracy. We present results for which the method successfully resolves Wood's anomaly resonances in transmission. Advisors/Committee Members: Beale, J T (advisor).

Subjects/Keywords: Mathematics; periodic scattering; singular integrals; photonic crystals

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APA (6^th Edition):

Nicholas, M. J. (2007). A Third Order Numerical Method for Doubly Periodic Electromegnetic Scattering . (Thesis). Duke University. Retrieved from http://hdl.handle.net/10161/383

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Nicholas, Michael J. “A Third Order Numerical Method for Doubly Periodic Electromegnetic Scattering .” 2007. Thesis, Duke University. Accessed April 12, 2021. http://hdl.handle.net/10161/383.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Nicholas, Michael J. “A Third Order Numerical Method for Doubly Periodic Electromegnetic Scattering .” 2007. Web. 12 Apr 2021.

Vancouver:

Nicholas MJ. A Third Order Numerical Method for Doubly Periodic Electromegnetic Scattering . [Internet] [Thesis]. Duke University; 2007. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/10161/383.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Nicholas MJ. A Third Order Numerical Method for Doubly Periodic Electromegnetic Scattering . [Thesis]. Duke University; 2007. Available from: http://hdl.handle.net/10161/383

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

20. Wala, Mateusz Michal. High-order numerical methods for layer potential evaluation.

Degree: PhD, Computer Science, 2019, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/106232

► This thesis addresses a number of obstacles in the practical realization of integral equation methods for boundary value problems of elliptic partial differential equations. Layer… (more)

▼ This thesis addresses a number of obstacles in the practical realization of integral equation methods for boundary value problems of elliptic partial differential equations. Layer potentials play a central role in the integral equation formulation of boundary value problems. However, the numerical evaluation of layer potentials presents significant practical challenges associated with issues of singular/near-singular quadrature and efficient scaling. Quadrature by Expansion (QBX) is a quadrature method that addresses many of the issues encountered in the evaluation of layer potentials, by providing a high-order and kernel/dimension independent quadrature scheme that is also acceleration-compatible, i.e., able to be integrated with a fast summation scheme to reduce the cost of O(N²) pairwise interactions to O(N). The focus of the first part of this thesis is an acceleration scheme for QBX based on the Fast Multipole Method (FMM) that provides both high performance and strong accuracy guarantees for mathematical control over the error introduced by acceleration. The scheme extends to both two and three dimensions and Laplace and Helmholtz kernels. The contribution in this thesis also includes a geometry processing framework to prepare arbitrary smooth geometries for accurate quadrature with QBX, a comprehensive complexity and error analysis of the algorithm, and a cost model and study of key optimizations. This thesis also considers the application of layer potentials to the problem of numerical conformal mapping. It is shown how there is a strong connection between the double-layer potential and the Faber/Faber-Laurent polynomials, which are polynomials closely related to the series expansion of the Riemann map. From this, a scheme for computing the Riemann map of a piecewise smooth Jordan domain is devised. This latter work also provides an insight into the convergence behavior of QBX. Finally, this thesis describes a software abstraction for the design and implementation of time integration algorithms for the solution of initial value problems. This abstraction, Dagrt, has two aims. The first is a epresentation that decouples the mathematical specification of a time integration algorithm from its realization in a particular programming model, and the second is to give the user control over implementation details. We demonstrate the capabilities of this abstraction by presenting Leap, a collection of pre-written time integration algorithm specifications that includes complex multistep and multistage methods. Advisors/Committee Members: Klöckner, Andreas (advisor), Klöckner, Andreas (Committee Chair), Olson, Luke (committee member), Fischer, Paul (committee member), Greengard, Leslie (committee member).

Subjects/Keywords: integral equations; layer potentials; fast multipole method; singular integrals; quadrature by expansion; conformal mapping; time integration

11 more images…

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APA (6^th Edition):

Wala, M. M. (2019). High-order numerical methods for layer potential evaluation. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/106232

Chicago Manual of Style (16^th Edition):

Wala, Mateusz Michal. “High-order numerical methods for layer potential evaluation.” 2019. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed April 12, 2021. http://hdl.handle.net/2142/106232.

MLA Handbook (7^th Edition):

Wala, Mateusz Michal. “High-order numerical methods for layer potential evaluation.” 2019. Web. 12 Apr 2021.

Vancouver:

Wala MM. High-order numerical methods for layer potential evaluation. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2019. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/2142/106232.

Council of Science Editors:

Wala MM. High-order numerical methods for layer potential evaluation. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2019. Available from: http://hdl.handle.net/2142/106232

Université Paris-Sud – Paris XI

21. Salles, Nicolas. Calcul des singularités dans les méthodes d’équations intégrales variationnelles : Calculation of singularities in variational integral equations methods.

Degree: Docteur es, Mathématiques appliquées, 2013, Université Paris-Sud – Paris XI

URL: http://www.theses.fr/2013PA112164

►

La mise en œuvre de la méthode des éléments finis de frontière nécessite l'évaluation d'intégrales comportant un intégrand singulier. Un calcul fiable et précis de… (more)

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La mise en œuvre de la méthode des éléments finis de frontière nécessite l'évaluation d'intégrales comportant un intégrand singulier. Un calcul fiable et précis de ces intégrales peut dans certains cas se révéler à la fois crucial et difficile. La méthode que nous proposons consiste en une réduction récursive de la dimension du domaine d'intégration et aboutit à une représentation de l'intégrale sous la forme d'une combinaison linéaire d'intégrales mono-dimensionnelles dont l'intégrand est régulier et qui peuvent s'évaluer numériquement mais aussi explicitement. L'équation de Helmholtz 3-D sert d'équation modèle mais ces résultats peuvent être utilisés pour les équations de Laplace et de Maxwell 3-D. L'intégrand est décomposé en une partie homogène et une partie régulière ; cette dernière peut être traitée par les méthodes usuelles d'intégration numérique. Pour la discrétisation du domaine, des triangles plans sont utilisés ; par conséquent, nous évaluons des intégrales sur le produit de deux triangles. La technique que nous avons développée nécessite de distinguer entre diverses configurations géométriques ; c'est pourquoi nous traitons séparément le cas de triangles coplanaires, dans des plans sécants ou parallèles. Divers prolongements significatifs de la méthode sont présentés : son extension à l'électromagnétisme, l'évaluation de l'intégrale du noyau de Green complet pour les coefficients d'auto-influence, et le calcul de la partie finie d'intégrales hypersingulières.

The implementation of the boundary element method requires the evaluation of integrals with a singular integrand. A reliable and accurate calculation of these integrals can in some cases be crucial and difficult. The proposed method is a recursive reduction of the dimension of the integration domain and leads to a representation of the integral as a linear combination of one-dimensional integrals whose integrand is regular and that can be evaluated numerically and even explicitly. The 3-D Helmholtz equation is used as a model equation, but these results can be used for the Laplace and the Maxwell equations in 3-D. The integrand is decomposed into a homogeneous part and a regular part, the latter can be treated by conventional numerical integration methods. For the discretization of the domain we use planar triangles, so we evaluate integrals over the product of two triangles. The technique we have developped requires to distinguish between several geometric configurations, that's why we treat separately the case of triangles in the same plane, in secant planes and in parallel planes.

Advisors/Committee Members: Bécache, Eliane (thesis director), Lenoir, Marc (thesis director).

Subjects/Keywords: Intégrales singulières; Méthode des éléments finis de frontière; Équation de Helmholtz; Fonctions homogènes; Singular integrals; Boundary element method; Helmholtz equation; Homogeneous functions

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Salles, N. (2013). Calcul des singularités dans les méthodes d’équations intégrales variationnelles : Calculation of singularities in variational integral equations methods. (Doctoral Dissertation). Université Paris-Sud – Paris XI. Retrieved from http://www.theses.fr/2013PA112164

Chicago Manual of Style (16^th Edition):

Salles, Nicolas. “Calcul des singularités dans les méthodes d’équations intégrales variationnelles : Calculation of singularities in variational integral equations methods.” 2013. Doctoral Dissertation, Université Paris-Sud – Paris XI. Accessed April 12, 2021. http://www.theses.fr/2013PA112164.

MLA Handbook (7^th Edition):

Salles, Nicolas. “Calcul des singularités dans les méthodes d’équations intégrales variationnelles : Calculation of singularities in variational integral equations methods.” 2013. Web. 12 Apr 2021.

Vancouver:

Salles N. Calcul des singularités dans les méthodes d’équations intégrales variationnelles : Calculation of singularities in variational integral equations methods. [Internet] [Doctoral dissertation]. Université Paris-Sud – Paris XI; 2013. [cited 2021 Apr 12]. Available from: http://www.theses.fr/2013PA112164.

Council of Science Editors:

Salles N. Calcul des singularités dans les méthodes d’équations intégrales variationnelles : Calculation of singularities in variational integral equations methods. [Doctoral Dissertation]. Université Paris-Sud – Paris XI; 2013. Available from: http://www.theses.fr/2013PA112164

Universitat Politècnica de Catalunya

22. Tamayo Palau, José María. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.

Degree: Departament de Teoria del Senyal i Comunicacions, 2011, Universitat Politècnica de Catalunya

URL: http://hdl.handle.net/10803/6952

► The Method of Moments (MoM) has been widely used during the last decades for the discretization and the solution of integral equation formulations appearing in… (more)

▼ The Method of Moments (MoM) has been widely used during the last decades for the discretization and the solution of integral equation formulations appearing in several electromagnetic antenna and scattering problems. The most utilized of these formulations are the Electric Field Integral Equation (EFIE), the Magnetic Field Integral Equation (MFIE) and the Combined Field Integral Equation (CFIE), which is a linear combination of the other two. The MFIE and CFIE formulations are only valid for closed objects and need to deal with the integration of singular kernels with singularities of higher order than the EFIE. The lack of efficient and accurate techniques for the computation of these singular integrals has led to inaccuracies in the results. Consequently, their use has been mainly restricted to academic purposes, even having a much better convergence rate when solved iteratively, due to their excellent conditioning number. In general, the main drawback of the MoM is the costly construction, storage and solution considering the unavoidable dense linear system, which grows with the electrical size of the object to analyze. Consequently, a wide range of fast methods have been developed for its compression and solution. Most of them, though, are absolutely dependent on the kernel of the integral equation, claiming for a complete re-formulation, if possible, for each new kernel. This thesis dissertation presents new approaches to accelerate or increase the accuracy of integral equations discretized by the Method of Moments (MoM) in computational electromagnetics. Firstly, a novel fast iterative solver, the Multilevel Adaptive Cross Approximation (MLACA), has been developed for accelerating the solution of the MoM linear system. In the quest for a general-purpose scheme, the MLACA is a method independent of the kernel of the integral equation and is purely algebraic. It improves both efficiency and compression rate with respect to the previously existing single-level version, the ACA. Therefore, it represents an excellent alternative for the solution of the MoM system of large-scale electromagnetic problems. Secondly, the direct evaluation method, which has proved to be the main reference in terms of efficiency and accuracy, is extended to overcome the computation of the challenging 4-D hyper-singular integrals arising in the Magnetic Field Integral Equation (MFIE) and Combined Field Integral Equation (CFIE) formulations. The maximum affordable accuracy – machine precision – is obtained in a more than reasonable computation time, surpassing any other existing technique in the literature. Thirdly, the aforementioned hyper-singular integrals become near-singular when the discretized elements are very closely placed but not touching. It is shown how traditional integration rules fail to converge also in this case, and a possible solution based on more sophisticated integration rules, like the Double Exponential and the Gauss-Laguerre, is proposed. Finally, an effort to facilitate the… Advisors/Committee Members: [email protected] (authoremail), false (authoremailshow), Rius Casals, Juan Manuel (director).

Subjects/Keywords: vertex adjacent integration; edge adjacent integration; adaptive cross approximation; impedance matrix compression; electromagnetism; numerical simulation; singular integrals; surface integral equations; fast solvers; method of moments (MOM); 517; 621.3

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APA (6^th Edition):

Tamayo Palau, J. M. (2011). Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. (Thesis). Universitat Politècnica de Catalunya. Retrieved from http://hdl.handle.net/10803/6952

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Tamayo Palau, José María. “Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.” 2011. Thesis, Universitat Politècnica de Catalunya. Accessed April 12, 2021. http://hdl.handle.net/10803/6952.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Tamayo Palau, José María. “Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations.” 2011. Web. 12 Apr 2021.

Vancouver:

Tamayo Palau JM. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. [Internet] [Thesis]. Universitat Politècnica de Catalunya; 2011. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/10803/6952.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Tamayo Palau JM. Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations. [Thesis]. Universitat Politècnica de Catalunya; 2011. Available from: http://hdl.handle.net/10803/6952

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

23. Oueslati, Soumaya. Une nouvelle formulation variationnelle pour le problème de diffusion en électromagnétisme utilisant une méthode intégrale avec une condition aux limites d'impédance d'ordre élevé - Petites perturbations d'une interface pour le système de Stokes : A new variational formulation for electromagnetic scatteringproblem using integral method with high order impedance boundarycondition - Small perturbations of an interface for Stokes system.

Degree: Docteur es, Mathématiques - EM2PSI, 2019, Cergy-Pontoise; École polytechnique de Tunisie (La Marsa)

URL: http://www.theses.fr/2019CERG1046

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Cette thèse contient deux parties principales. Dans la première partie, nous proposons une nouvelle formulation variationnelle pour le problème de diffusion en électromagnétisme qui s’obtient… (more)

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Cette thèse contient deux parties principales. Dans la première partie, nous proposons une nouvelle formulation variationnelle pour le problème de diffusion en électromagnétisme qui s’obtient avec une méthode intégrale utilisant une condition aux limites d’impédance d’ordre élevé (HOIBC). Cette méthode améliore la précision du calcul de la surface équivalente radar (SER) par rapport à la condition limite d’impédance de Leontovich dans de nombreux cas. Ensuite, nous donnons la discrétisation de cette formulation avec des fonctions de base de Rao-Wilton-Glisson. Par suite, une approximation de la condition aux limites d’impédance d’ordre élevé est donnée. A cette fin, des formules de saut et la théorie des distributions pour surmonter la difficulté de la discrétisation de div(n×w) et de rot(w) pour tout w dans H(div) est utilisée. De plus, nous mettons en oeuvre trois méthodes pour évaluer certaines intégrales singulières qui apparaissent dans les éléments de matrice de notre formulation. Cette méthode numérique est validée par des cas tests sur des sphères où l'on compare les résultats numériques et analytiques pour le calcul de la SER. Dans la deuxième partie, on a étudié un problème de transmission pour le système de Stokes. Tout d’abord, on a trouvé une représentation de la solution en appliquant la théorie du potentiel. Par la suite, on a obtenu un développement asymptotique de cette solution en fonction du paramètre de la déformation du bord de l’inclusion. Puis, on a donné un développement asymptotique pour le tenseur de viscosité du système de Stokes.

This thesis contains two main parts. In the first one, we propose a new variational formulation for the electromagnetic scattering problem which derives from an integral method with the use of high order impedance boundary condition (HOIBC) to improve the accuracy of Leontovich impedance boundary condition. Then, we give the discretization for this formulation with Rao-Wilton-Glisson basis functions. Therefore, we propose an approximation of the high order impedance boundary condition which is Hodge operator. We use the jump formulas and the theory of distributions to overcome the difficulty of the discretization of div(n × w) and rot(w) for all w in H(div). Moreover, we implement three methods to evaluate some singular integrals that appear in the boundary integral equation. The performances of the HOIBC are evaluated by calculating the radar cross section (RCS) with different meshes for the unit sphere. We also compare the numerical and analytical results. In the second part, we have considered the Stokes system for a viscous medium consisting of an inclusion immerged in a background medium. We derive the asymptotic expansion of the perturbed velocity field due to the presence of small perturbations in the interface of an inclusion using the layer potential theory. Further, we use these techniques to determine a relationship between Stokes solutions measurements and the shape of the object. Besides, we prove an asymptotic expansion for the perturbation in the…

Advisors/Committee Members: Daveau, Christian (thesis director), Khelifi, Abdessatar (thesis director).

Subjects/Keywords: Intégrales singulières; Dévloppement asymtotique; Contion aux limites d'impédance d'ordre élevé; Tenseurs de viscosité; Système de Stokes; Singular integrals; Stokes system; Viscous moment tensors; High order impedance boundary condition; Asymptotic expansions

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Oueslati, S. (2019). Une nouvelle formulation variationnelle pour le problème de diffusion en électromagnétisme utilisant une méthode intégrale avec une condition aux limites d'impédance d'ordre élevé - Petites perturbations d'une interface pour le système de Stokes : A new variational formulation for electromagnetic scatteringproblem using integral method with high order impedance boundarycondition - Small perturbations of an interface for Stokes system. (Doctoral Dissertation). Cergy-Pontoise; École polytechnique de Tunisie (La Marsa). Retrieved from http://www.theses.fr/2019CERG1046

Chicago Manual of Style (16^th Edition):

Oueslati, Soumaya. “Une nouvelle formulation variationnelle pour le problème de diffusion en électromagnétisme utilisant une méthode intégrale avec une condition aux limites d'impédance d'ordre élevé - Petites perturbations d'une interface pour le système de Stokes : A new variational formulation for electromagnetic scatteringproblem using integral method with high order impedance boundarycondition - Small perturbations of an interface for Stokes system.” 2019. Doctoral Dissertation, Cergy-Pontoise; École polytechnique de Tunisie (La Marsa). Accessed April 12, 2021. http://www.theses.fr/2019CERG1046.

MLA Handbook (7^th Edition):

Oueslati, Soumaya. “Une nouvelle formulation variationnelle pour le problème de diffusion en électromagnétisme utilisant une méthode intégrale avec une condition aux limites d'impédance d'ordre élevé - Petites perturbations d'une interface pour le système de Stokes : A new variational formulation for electromagnetic scatteringproblem using integral method with high order impedance boundarycondition - Small perturbations of an interface for Stokes system.” 2019. Web. 12 Apr 2021.

Vancouver:

Oueslati S. Une nouvelle formulation variationnelle pour le problème de diffusion en électromagnétisme utilisant une méthode intégrale avec une condition aux limites d'impédance d'ordre élevé - Petites perturbations d'une interface pour le système de Stokes : A new variational formulation for electromagnetic scatteringproblem using integral method with high order impedance boundarycondition - Small perturbations of an interface for Stokes system. [Internet] [Doctoral dissertation]. Cergy-Pontoise; École polytechnique de Tunisie (La Marsa); 2019. [cited 2021 Apr 12]. Available from: http://www.theses.fr/2019CERG1046.

Council of Science Editors:

Oueslati S. Une nouvelle formulation variationnelle pour le problème de diffusion en électromagnétisme utilisant une méthode intégrale avec une condition aux limites d'impédance d'ordre élevé - Petites perturbations d'une interface pour le système de Stokes : A new variational formulation for electromagnetic scatteringproblem using integral method with high order impedance boundarycondition - Small perturbations of an interface for Stokes system. [Doctoral Dissertation]. Cergy-Pontoise; École polytechnique de Tunisie (La Marsa); 2019. Available from: http://www.theses.fr/2019CERG1046

24. Parissis, Ioannis. Oscillatory integrals with polynomial phase.

Degree: 2007, University of Crete (UOC); Πανεπιστήμιο Κρήτης

URL: http://hdl.handle.net/10442/hedi/31927

Subjects/Keywords: Ολοκληρώματα ταλάντωσης; Αρμονική ανάλυση; Πολυωνυμική φάση; Oscillatory integrals; Harmonic analysis; Polynomial phase; Singular oscillatory integrals

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Parissis, I. (2007). Oscillatory integrals with polynomial phase. (Thesis). University of Crete (UOC); Πανεπιστήμιο Κρήτης. Retrieved from http://hdl.handle.net/10442/hedi/31927

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Parissis, Ioannis. “Oscillatory integrals with polynomial phase.” 2007. Thesis, University of Crete (UOC); Πανεπιστήμιο Κρήτης. Accessed April 12, 2021. http://hdl.handle.net/10442/hedi/31927.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Parissis, Ioannis. “Oscillatory integrals with polynomial phase.” 2007. Web. 12 Apr 2021.

Vancouver:

Parissis I. Oscillatory integrals with polynomial phase. [Internet] [Thesis]. University of Crete (UOC); Πανεπιστήμιο Κρήτης; 2007. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/10442/hedi/31927.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Parissis I. Oscillatory integrals with polynomial phase. [Thesis]. University of Crete (UOC); Πανεπιστήμιο Κρήτης; 2007. Available from: http://hdl.handle.net/10442/hedi/31927

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

25. Bosch Camós, Anna. Controlant la integral singular maximal.

Degree: Departament de Matemàtiques, 2015, Universitat Autònoma de Barcelona

URL: http://hdl.handle.net/10803/314177

► The main objects of study of this dissertation are the singular integrals. We find an special motivation in three papers originated from the idea of… (more)

▼ The main objects of study of this dissertation are the singular integrals. We find an special motivation in three papers originated from the idea of bounding the norm of maximal operator of a singular integral by the norm of the singular integral itself. In the first one, of J. Mateu and J. Verdera from 2006, [MV], they prove pointwise inequalities for the particular cases of the j-th Riesz transform and the Beurling transform. For the first time, one notice that we obtain different bounds depending on the parity of the kernel of each operator. A posteriori, in the papers of J. Mateu, J. Orobitg and J. Verdera from 2011, [MOV], and in [MOPV] from 2010 from same authors plus C. Pérez, they prove pointwise inequalities as the aforementioned for higher order Riesz transforms. In the first work they treat the case of operators with even kernel, and in the second one, they do the same but for odd kernels. Here is when Cotlar inequality takes shows of, because we can notice that the inequality for the even case is an improvement of this one In [MOV] they prove that, for even Calderón-Zygmund singular integrals with smooth kernel, the pointwise inequality of the maximal operator bounded by the operator itself is equivalent to the L² estimate and also to an algebraic condition on the kernel of the singular integral. For the odd operators, in [MOPV], it's proved the same result, but in the pointwise inequality we need the second iteration of the Hardy-Littlewood maximal operator. It was proved before, in [MV], that one cannot bound without this iteration in the case of the Riesz trasnform. From here on, in this dissertation we have been working on this kind of estimates. In the first chapter we give a positive answer to one open question in [MOV]. We prove that the L^p estimate (and the weighted L^p) is also equivalent to the pointwise inequality, not only with p=2. This results are reflected in [BMO1]. In the second chapter we work on another open question from the same paper. We deal with the same estimates but relaxing the regularity of the kernel. When we are in the plane, we give a good answer, setting an initial differenciability for the kernel. For higher dimensions, with n bigger than 2, we have a partial answer, in the sense that the initial regularity depends on the degree of a polynomial depending on the kernel. This means that we may should ask for a very big differentiability, but a finite one. In the third chapter, we give an example for which we can't bound de weak L¹ norm of the maximal function in terms of the L¹ norm of the operator. We give the case of a harmonic polynomial of degree 3 in the plane and we explain how we can generalize to all polynomials with odd degree in the plane. However, because of the difficult caracterization of the harmonic polynomials en higher dimensions, the problem in Rⁿ, for n>2, is open. In the last chapter, we consider the same problem of pointwise estimating the maximal operator of a singular integral by the same operator, but in this case we define a… Advisors/Committee Members: [email protected] (authoremail), true (authoremailshow), Mateu Bennassar, Joan Eugeni (director), Orobitg i Huguet, Joan (director), true (authorsendemail).

Subjects/Keywords: Integrals singulars; Singular integrals; Integrales singulares; Operador maximal; Maximal operator; Operador maximal; Ciències Experimentals; 517

…condició algebraica sobre el nucli de la integral singular. 3 En el cas de les integrals de… …Introducció Els principals objectes d’estudi d’aquesta memòria són les integrals… …potencial. Les primeres integrals singulars que es van considerar eren al pla, com la funció… …conjugada, que és una integral singular al tor unidimensional, per això s’utilitzava l’an� lisi… …complexa per resoldre els problemes d’acotació d’aquestes integrals. En una segona fase, Antoni…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bosch Camós, A. (2015). Controlant la integral singular maximal. (Thesis). Universitat Autònoma de Barcelona. Retrieved from http://hdl.handle.net/10803/314177

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Bosch Camós, Anna. “Controlant la integral singular maximal.” 2015. Thesis, Universitat Autònoma de Barcelona. Accessed April 12, 2021. http://hdl.handle.net/10803/314177.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Bosch Camós, Anna. “Controlant la integral singular maximal.” 2015. Web. 12 Apr 2021.

Vancouver:

Bosch Camós A. Controlant la integral singular maximal. [Internet] [Thesis]. Universitat Autònoma de Barcelona; 2015. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/10803/314177.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bosch Camós A. Controlant la integral singular maximal. [Thesis]. Universitat Autònoma de Barcelona; 2015. Available from: http://hdl.handle.net/10803/314177

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Indian Institute of Science

26. George, A J. A Study On Solutions Of Singular Integral Equations.

Degree: PhD, Faculty of Science, 2012, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/1736

Subjects/Keywords: Singularities; Integral Equations; Operational Calculus; Integral Transforms; Functional Analysis; Singular Integral Equation; Singular Integrals; Singular Integral Equation Theory; Fractional Calculus; Abel Integral Equation; Abel-Integral Operators; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

George, A. J. (2012). A Study On Solutions Of Singular Integral Equations. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/1736

Chicago Manual of Style (16^th Edition):

George, A J. “A Study On Solutions Of Singular Integral Equations.” 2012. Doctoral Dissertation, Indian Institute of Science. Accessed April 12, 2021. http://etd.iisc.ac.in/handle/2005/1736.

MLA Handbook (7^th Edition):

George, A J. “A Study On Solutions Of Singular Integral Equations.” 2012. Web. 12 Apr 2021.

Vancouver:

George AJ. A Study On Solutions Of Singular Integral Equations. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2012. [cited 2021 Apr 12]. Available from: http://etd.iisc.ac.in/handle/2005/1736.

Council of Science Editors:

George AJ. A Study On Solutions Of Singular Integral Equations. [Doctoral Dissertation]. Indian Institute of Science; 2012. Available from: http://etd.iisc.ac.in/handle/2005/1736

27. [No author]. Boundary Measures and Cubical Covers of Sets in R^n .

Degree: 2018, Washington State University

URL: http://hdl.handle.net/2376/16417

► The art of analysis involves the subtle combination of approximation, inequalities, and geometric intuition as well as being able to work at different scales. Even… (more)

Subjects/Keywords: Mathematics; Cubical Covers; Geometric Measure Theory; Hausdorff Measure; Real Analysis; Singular Integrals; Varifolds

…Description of Singular Integrals Singular integrals are central to harmonic analysis [53]… …the similarities are worth noting. The most well known examples of singular integrals in… …The singular integrals mentioned thus far are of convolution type, and in the case of the… …development of the singular integral boundary measure for hypersurfaces in Rn , presented below, and… …present a singular integral that measures the (n − 1)-dimensional Hausdorff measure Hn…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

author], [. (2018). Boundary Measures and Cubical Covers of Sets in R^n . (Thesis). Washington State University. Retrieved from http://hdl.handle.net/2376/16417

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

author], [No. “Boundary Measures and Cubical Covers of Sets in R^n .” 2018. Thesis, Washington State University. Accessed April 12, 2021. http://hdl.handle.net/2376/16417.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

author], [No. “Boundary Measures and Cubical Covers of Sets in R^n .” 2018. Web. 12 Apr 2021.

Vancouver:

author] [. Boundary Measures and Cubical Covers of Sets in R^n . [Internet] [Thesis]. Washington State University; 2018. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/2376/16417.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

author] [. Boundary Measures and Cubical Covers of Sets in R^n . [Thesis]. Washington State University; 2018. Available from: http://hdl.handle.net/2376/16417

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

28. Gao, Hao. Layer potential evaluations on distributed memory machines.

Degree: MS, Computer Science, 2020, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/108032

► One of the main challenges of using integral equation methods (IEM) for solving partial differential equations is evaluating layer potentials with singular kernels. Quadrature by… (more)

Subjects/Keywords: Layer Potentials; Distributed Memory Parallelism; Integral Equations; Singular Integrals; Fast Multipole Method

…total number of quadrature nodes is 200. with singular kernels at target points near or on the… …kernel and Gaussian quadrature as an example, QBX can be used for evaluating other singular… …critical to evaluate layer potentials, usually with singular kernels, efficiently and accurately…

6 more images…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gao, H. (2020). Layer potential evaluations on distributed memory machines. (Thesis). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/108032

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Gao, Hao. “Layer potential evaluations on distributed memory machines.” 2020. Thesis, University of Illinois – Urbana-Champaign. Accessed April 12, 2021. http://hdl.handle.net/2142/108032.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Gao, Hao. “Layer potential evaluations on distributed memory machines.” 2020. Web. 12 Apr 2021.

Vancouver:

Gao H. Layer potential evaluations on distributed memory machines. [Internet] [Thesis]. University of Illinois – Urbana-Champaign; 2020. [cited 2021 Apr 12]. Available from: http://hdl.handle.net/2142/108032.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gao H. Layer potential evaluations on distributed memory machines. [Thesis]. University of Illinois – Urbana-Champaign; 2020. Available from: http://hdl.handle.net/2142/108032

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

29. Dalcy, Muriel Andreane. Teoria dos operadores integrais singulares.

Degree: 2020, Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar

URL: https://repositorio.ufscar.br/handle/ufscar/12948

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

We present in this work some of the main results regarding the continuity in Lp and… (more)

Subjects/Keywords: Análise harmônica; Integrais singulares; Decomposição de Calderón-Zygmund; Transformada de Riesz; Harmonic analysis; Singular integrals; Calderón-Zygmund decomposition; Riesz transform; CIENCIAS EXATAS E DA TERRA::MATEMATICA; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Dalcy, M. A. (2020). Teoria dos operadores integrais singulares. (Masters Thesis). Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar. Retrieved from https://repositorio.ufscar.br/handle/ufscar/12948

Chicago Manual of Style (16^th Edition):

Dalcy, Muriel Andreane. “Teoria dos operadores integrais singulares.” 2020. Masters Thesis, Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar. Accessed April 12, 2021. https://repositorio.ufscar.br/handle/ufscar/12948.

MLA Handbook (7^th Edition):

Dalcy, Muriel Andreane. “Teoria dos operadores integrais singulares.” 2020. Web. 12 Apr 2021.

Vancouver:

Dalcy MA. Teoria dos operadores integrais singulares. [Internet] [Masters thesis]. Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar; 2020. [cited 2021 Apr 12]. Available from: https://repositorio.ufscar.br/handle/ufscar/12948.

Council of Science Editors:

Dalcy MA. Teoria dos operadores integrais singulares. [Masters Thesis]. Universidade Federal de São Carlos; Câmpus São Carlos; Programa de Pós-Graduação em Matemática – PPGM; UFSCar; 2020. Available from: https://repositorio.ufscar.br/handle/ufscar/12948

30. Cambon, Sebastien. Méthode d'éléments finis d'ordre élevé et d'équations intégrales pour la résolution de problème de furtivité radar d'objets à symétrie de révolution : High order finite element methods and integral equations to solve scattering problems by axisymmetric bodies.

Degree: Docteur es, Mathématiques Appliquées, 2012, Toulouse, INSA

URL: http://www.theses.fr/2012ISAT0047

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Dans ce travail de thèse, nous nous sommes intéressés à la modélisation des phénomènes de diffraction d’ondes électromagnétiques par des objets à symétrie de révolution… (more)

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Dans ce travail de thèse, nous nous sommes intéressés à la modélisation des phénomènes de diffraction d’ondes électromagnétiques par des objets à symétrie de révolution complexes et fortement hétérogènes. La méthode que nous développons ici consiste en un couplage entre équations aux dérivées partielles (EDP) et équations intégrales (EI). Cette idée est essentiellement connue pour avoir deux avantages. Le premier est que les hétérogénéités de l’objet sont prises en compte naturellement dans la formulation du problème. Le deuxième est dû à l’utilisation des équations intégrales qui donnent une représentation exacte des solutions dans le milieu extérieur en fonction des courants surfaciques. Le domaine de simulation peut ainsi être ramené à l’objet lui-même. L’utilisation de développements en séries de Fourier combinés à la propriété d’invariance par rotation de l’objet permet alors la réduction du problème global 3D à un ensemble dénombrable de problème 2D.L’étude de ces problèmes nous a conduit à décomposer notre analyse en plusieurs parties,chacune ayant à traiter une partie du problème complet ou les méthodes d’intégrations numériques. Ces dernières étant difficiles à réaliser dans le cas des équations intégrales.Nous avons tout d’abord étudié un problème de Maxwell intérieur pour lequel nous avons développé une nouvelle méthode d’éléments finis d’ordre élevé dont nous avons montré l’efficacité et la précision sur de multiples exemples. Puis, nous avons étudié le problème de diffraction d’ondes planes pour des objets parfaitement conducteurs. La méthode d’éléments finis de frontière employée est alors construite par extension de la méthode précédente via l’opérateur de trace tangentielle. En combinant ces deux études, nous avons résolu le problème couplé en introduisant la propriété de symétrie de révolution dans une formulation variationnelle bien choisie. Par construction, les éléments finis qui y sont utilisés sont alors naturellement adaptées. L’algorithme de parallélisation de la méthode de couplage est finalement présentée et des comparaisons entre notre code AxiMax et un code 3D sont illustrées. Dans tous les cas, nous montrons que la méthode d’éléments finis d’ordre élevé permet d’obtenir des résultats d’une grande précision en fonction de la qualité des paramètres de simulation.

In this thesis, we are interested in modeling diffraction of electromagnetic waves by axisymmetric and highly heterogeneous objects. Our method consists in a coupling between partial differential equations and integral equations. This idea is mainly interesting for two reasons : heterogeneities are handled naturally in the formulation and integral equations give an analytical representation of solutions outside the object based on surface currents.These advantages allow us to limit the domain of simulation to the object itself. In addition,using Fourier series combined with the rotational invariance property of the object, the 3D problem is reduced to a countable set of 2D problems. The study of these problems is split into…

Advisors/Committee Members: Bonnet-Ben Dhia, Anne-Sophie (thesis director).

Subjects/Keywords: Électromagnétisme; Équations de Maxwell; Harmoniques; Équations intégrales; Intégration numérique d’intégrales singulières; Éléments finis d’ordre élevé; Symétrie de révolution; Séries de Fourier; Couplage équations aux dérivées partielles et équations intégrales; Electromagnetism; Time harmonic Maxwell’s equations; Integral equations; High-order finite element; Symmetry of revolution; Fourier series; Coupling method; Singular integrals; 537

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Cambon, S. (2012). Méthode d'éléments finis d'ordre élevé et d'équations intégrales pour la résolution de problème de furtivité radar d'objets à symétrie de révolution : High order finite element methods and integral equations to solve scattering problems by axisymmetric bodies. (Doctoral Dissertation). Toulouse, INSA. Retrieved from http://www.theses.fr/2012ISAT0047

Chicago Manual of Style (16^th Edition):

Cambon, Sebastien. “Méthode d'éléments finis d'ordre élevé et d'équations intégrales pour la résolution de problème de furtivité radar d'objets à symétrie de révolution : High order finite element methods and integral equations to solve scattering problems by axisymmetric bodies.” 2012. Doctoral Dissertation, Toulouse, INSA. Accessed April 12, 2021. http://www.theses.fr/2012ISAT0047.

MLA Handbook (7^th Edition):

Cambon, Sebastien. “Méthode d'éléments finis d'ordre élevé et d'équations intégrales pour la résolution de problème de furtivité radar d'objets à symétrie de révolution : High order finite element methods and integral equations to solve scattering problems by axisymmetric bodies.” 2012. Web. 12 Apr 2021.

Vancouver:

Cambon S. Méthode d'éléments finis d'ordre élevé et d'équations intégrales pour la résolution de problème de furtivité radar d'objets à symétrie de révolution : High order finite element methods and integral equations to solve scattering problems by axisymmetric bodies. [Internet] [Doctoral dissertation]. Toulouse, INSA; 2012. [cited 2021 Apr 12]. Available from: http://www.theses.fr/2012ISAT0047.

Council of Science Editors:

Cambon S. Méthode d'éléments finis d'ordre élevé et d'équations intégrales pour la résolution de problème de furtivité radar d'objets à symétrie de révolution : High order finite element methods and integral equations to solve scattering problems by axisymmetric bodies. [Doctoral Dissertation]. Toulouse, INSA; 2012. Available from: http://www.theses.fr/2012ISAT0047

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