subject:(Dirac operators)

Australian National University

1. Morris, Andrew Jordan. Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds .

Degree: 2010, Australian National University

URL: http://hdl.handle.net/1885/8864

► The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to… (more)

▼ The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to the theory of differential operators. This is a generalization of the connection between Littlewood – Paley – Stein estimates and the functional calculus provided by the Fourier transform. We use the former approach in this thesis to study first-order differential operators on Riemannian manifolds. The theory developed is local in the sense that it does not depend on the spectrum of the operator in a neighbourhood of the origin. When we apply harmonic analysis to obtain estimates, the local theory only requires that we do so up to a finite scale. This allows us to consider manifolds with exponential volume growth in situations where the global theory requires polynomial volume growth. A holomorphic functional calculus is constructed for operators on a reflexive Banach space that are bisectorial except possibly in a neighbourhood of the origin. We prove that this functional calculus is bounded if and only if certain local quadratic estimates hold. For operators with spectrum in a neighbourhood of the origin, the results are weaker than those for bisectorial operators. For operators with a spectral gap in a neighbourhood of the origin, the results are stronger. In each case, however, local quadratic estimates are a more appropriate tool than standard quadratic estimates for establishing that the functional calculus is bounded. This theory allows us to define local Hardy spaces of differential forms that are adapted to a class of first-order differential operators on a complete Riemannian manifold with at most exponential volume growth. The local geometric Riesz transform associated with the Hodge – Dirac operator is bounded on these spaces provided that a certain condition on the exponential growth of the manifold is satisfied. A characterisation of these spaces in terms of local molecules is also obtained. These results can be viewed as the localisation of those for the Hardy spaces of differential forms introduced by Auscher, McIntosh and Russ. Finally, we introduce a class of first-order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincaré inequality holds. A local quadratic estimate is established for certain perturbations of these operators. As an application, we solve the Kato square root problem for divergence form operators on complete Riemannian manifolds with Ricci curvature bounded below that are embedded in Euclidean space with a uniformly bounded second fundamental form. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.

Subjects/Keywords: holomorphic functional calculi; quadratic estimates; sectorial operators; local Hardy spaces; Riemannian manifolds; differential forms; Hodge – Dirac operators; local Riesz transforms; off-diagonal estimates; Davies – Gaffney estimates; Kato square-root problems; submanifolds; divergence form operators; first-order differential operators

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

APA (6^th Edition):

Morris, A. J. (2010). Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds . (Thesis). Australian National University. Retrieved from http://hdl.handle.net/1885/8864

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):

Morris, Andrew Jordan. “Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds .” 2010. Thesis, Australian National University. Accessed January 25, 2021. http://hdl.handle.net/1885/8864.

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

MLA Handbook (7^th Edition):

Morris, Andrew Jordan. “Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds .” 2010. Web. 25 Jan 2021.

Vancouver:

Morris AJ. Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds . [Internet] [Thesis]. Australian National University; 2010. [cited 2021 Jan 25]. Available from: http://hdl.handle.net/1885/8864.

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

Council of Science Editors:

Morris AJ. Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds . [Thesis]. Australian National University; 2010. Available from: http://hdl.handle.net/1885/8864

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

ETH Zürich

2. Farinelli, S. Spectra of dirac operators on a family of degenerating hyperbolic three manifolds.

Degree: 1998, ETH Zürich

URL: http://hdl.handle.net/20.500.11850/143641

Subjects/Keywords: DIRAC-OPERATOREN (FUNKTIONALANALYSIS); RIEMANNSCHE MANNIGFALTIGKEITEN (TOPOLOGIE); DIRAC OPERATORS (FUNCTIONAL ANALYSIS); RIEMANNIAN MANIFOLDS (TOPOLOGY); info:eu-repo/classification/ddc/510; info:eu-repo/classification/ddc/510; info:eu-repo/classification/ddc/510; Mathematics; Mathematics; Mathematics

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APA (6^th Edition):

Farinelli, S. (1998). Spectra of dirac operators on a family of degenerating hyperbolic three manifolds. (Doctoral Dissertation). ETH Zürich. Retrieved from http://hdl.handle.net/20.500.11850/143641

Chicago Manual of Style (16^th Edition):

Farinelli, S. “Spectra of dirac operators on a family of degenerating hyperbolic three manifolds.” 1998. Doctoral Dissertation, ETH Zürich. Accessed January 25, 2021. http://hdl.handle.net/20.500.11850/143641.

MLA Handbook (7^th Edition):

Farinelli, S. “Spectra of dirac operators on a family of degenerating hyperbolic three manifolds.” 1998. Web. 25 Jan 2021.

Vancouver:

Farinelli S. Spectra of dirac operators on a family of degenerating hyperbolic three manifolds. [Internet] [Doctoral dissertation]. ETH Zürich; 1998. [cited 2021 Jan 25]. Available from: http://hdl.handle.net/20.500.11850/143641.

Council of Science Editors:

Farinelli S. Spectra of dirac operators on a family of degenerating hyperbolic three manifolds. [Doctoral Dissertation]. ETH Zürich; 1998. Available from: http://hdl.handle.net/20.500.11850/143641

Indian Institute of Science

3. Rahaman, Md Aminoor. Search On A Hypercubic Lattice Using Quantum Random Walk.

Degree: MSc Engg, Faculty of Engineering, 2010, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/972

► Random walks describe diffusion processes, where movement at every time step is restricted only to neighbouring locations. Classical random walks are constructed using the non-relativistic… (more)

Subjects/Keywords: Lattice Theory - Data Processing; Quantum Random Walk; Grover's Algorithm; Dirac Operators; Quantum Computation; Dimensional Hypercubic Lattices; Random Walk Algorithm; Spatial Search; Quantum Physics

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APA (6^th Edition):

Rahaman, M. A. (2010). Search On A Hypercubic Lattice Using Quantum Random Walk. (Masters Thesis). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/972

Chicago Manual of Style (16^th Edition):

Rahaman, Md Aminoor. “Search On A Hypercubic Lattice Using Quantum Random Walk.” 2010. Masters Thesis, Indian Institute of Science. Accessed January 25, 2021. http://etd.iisc.ac.in/handle/2005/972.

MLA Handbook (7^th Edition):

Rahaman, Md Aminoor. “Search On A Hypercubic Lattice Using Quantum Random Walk.” 2010. Web. 25 Jan 2021.

Vancouver:

Rahaman MA. Search On A Hypercubic Lattice Using Quantum Random Walk. [Internet] [Masters thesis]. Indian Institute of Science; 2010. [cited 2021 Jan 25]. Available from: http://etd.iisc.ac.in/handle/2005/972.

Council of Science Editors:

Rahaman MA. Search On A Hypercubic Lattice Using Quantum Random Walk. [Masters Thesis]. Indian Institute of Science; 2010. Available from: http://etd.iisc.ac.in/handle/2005/972

4. Takata, Doman. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .

Degree: 2018, Kyoto University

URL: http://hdl.handle.net/2433/232217

Subjects/Keywords: infinite-dimensional manifolds; loop groups; Dirac operators; assembly maps; KK-theory; index theory

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APA (6^th Edition):

Takata, D. (2018). A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . (Thesis). Kyoto University. Retrieved from http://hdl.handle.net/2433/232217

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):

Takata, Doman. “A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .” 2018. Thesis, Kyoto University. Accessed January 25, 2021. http://hdl.handle.net/2433/232217.

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

MLA Handbook (7^th Edition):

Takata, Doman. “A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds .” 2018. Web. 25 Jan 2021.

Vancouver:

Takata D. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . [Internet] [Thesis]. Kyoto University; 2018. [cited 2021 Jan 25]. Available from: http://hdl.handle.net/2433/232217.

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

Council of Science Editors:

Takata D. A Loop Group Equivariant Analytic Index Theory for Infinite-dimensional Manifolds . [Thesis]. Kyoto University; 2018. Available from: http://hdl.handle.net/2433/232217

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

Loughborough University

5. Li, Liangpan. Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators.

Degree: PhD, 2016, Loughborough University

URL: http://hdl.handle.net/2134/23004

► In this dissertation we study non-negative self-adjoint Laplace type operators acting on smooth sections of a vector bundle. First, we assume base manifolds are compact,… (more)

▼ In this dissertation we study non-negative self-adjoint Laplace type operators acting on smooth sections of a vector bundle. First, we assume base manifolds are compact, boundaryless, and Riemannian. We start from the Fourier integral operator representation of half-wave operators, continue with spectral zeta functions, heat and resolvent trace asymptotic expansions, and end with the quantitative Wodzicki residue method. In particular, all of the asymptotic coefficients of the microlocalized spectral counting function can be explicitly given and clearly interpreted. With the auxiliary pseudo-differential operators ranging all smooth endomorphisms of the given bundle, we obtain certain asymptotic estimates about the integral kernel of heat operators. As applications, we study spectral asymptotics of Dirac type operators such as characterizing those for which the second coefficient vanishes. Next, we assume vector bundles are trivial and base manifolds are Euclidean domains, and study non-negative self-adjoint extensions of the Laplace operator which acts component-wise on compactly supported smooth functions. Using finite propagation speed estimates for wave equations and explicit Fourier Tauberian theorems obtained by Yuri Safarov, we establish the principle of not feeling the boundary estimates for the heat kernel of these operators. In particular, the implied constants are independent of self-adjoint extensions. As a by-product, we affirmatively answer a question about upper estimate for the Neumann heat kernel. Finally, we study some specific values of the spectral zeta function of two-dimensional Dirichlet Laplacians such as spectral determinant and Casimir energy. For numerical purposes we substantially improve the short-time Dirichlet heat trace asymptotics for polygons. This could be used to measure the spectral determinant and Casimir energy of polygons whenever the first several hundred or one thousand Dirichlet eigenvalues are known with high precision by other means.

Subjects/Keywords: 515; Local spectral asymptotics; Heat kernel; Dirac operators; Laplace operators; Pseudo-differential operators; Fourier integral operators; Wodzicki residue; Finite propagation speed; Spectral determinant

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

APA (6^th Edition):

Li, L. (2016). Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. (Doctoral Dissertation). Loughborough University. Retrieved from http://hdl.handle.net/2134/23004

Chicago Manual of Style (16^th Edition):

Li, Liangpan. “Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators.” 2016. Doctoral Dissertation, Loughborough University. Accessed January 25, 2021. http://hdl.handle.net/2134/23004.

MLA Handbook (7^th Edition):

Li, Liangpan. “Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators.” 2016. Web. 25 Jan 2021.

Vancouver:

Li L. Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. [Internet] [Doctoral dissertation]. Loughborough University; 2016. [cited 2021 Jan 25]. Available from: http://hdl.handle.net/2134/23004.

Council of Science Editors:

Li L. Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. [Doctoral Dissertation]. Loughborough University; 2016. Available from: http://hdl.handle.net/2134/23004

Michigan State University

6. Maridakis, Manousos. The concentration principle for Dirac operators.

Degree: 2014, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:2604

►

Thesis Ph. D. Michigan State University. Mathematics 2014.

The symbol map σ of an elliptic operator carries essential topological and geometrical information about the underlying… (more)

Subjects/Keywords: Dirac equation; Manifolds (Mathematics); Differential operators; Theoretical mathematics

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APA (6^th Edition):

Maridakis, M. (2014). The concentration principle for Dirac operators. (Thesis). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:2604

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):

Maridakis, Manousos. “The concentration principle for Dirac operators.” 2014. Thesis, Michigan State University. Accessed January 25, 2021. http://etd.lib.msu.edu/islandora/object/etd:2604.

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

MLA Handbook (7^th Edition):

Maridakis, Manousos. “The concentration principle for Dirac operators.” 2014. Web. 25 Jan 2021.

Vancouver:

Maridakis M. The concentration principle for Dirac operators. [Internet] [Thesis]. Michigan State University; 2014. [cited 2021 Jan 25]. Available from: http://etd.lib.msu.edu/islandora/object/etd:2604.

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

Council of Science Editors:

Maridakis M. The concentration principle for Dirac operators. [Thesis]. Michigan State University; 2014. Available from: http://etd.lib.msu.edu/islandora/object/etd:2604

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

7. Beheshti Vadeqan, Babak. Geometry of Dirac Operators .

Degree: Mathematics and Statistics, 2016, Queens University

URL: http://hdl.handle.net/1974/14633

► Let M be a compact, oriented, even dimensional Riemannian manifold and let S be a Clifford bundle over M with Dirac operator D. Then [… (more)

Subjects/Keywords: Atiyah-Singer Index Theorem ; Dirac Operators ; Elliptic Geometry

…this thesis to show that elliptic operators and specifically Dirac operators contain certain… …Dirac operators. We shall also see that the study of Dirac operators reveals some… …a more general type of elliptic differential operators which are said to be Dirac type… …operators called Dirac operators. In this thesis we are planning to study this type of operators… …Dirac operators on manifolds. We will start by introducing Clifford algebras and their…

1 more image…

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APA (6^th Edition):

Beheshti Vadeqan, B. (2016). Geometry of Dirac Operators . (Thesis). Queens University. Retrieved from http://hdl.handle.net/1974/14633

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):

Beheshti Vadeqan, Babak. “Geometry of Dirac Operators .” 2016. Thesis, Queens University. Accessed January 25, 2021. http://hdl.handle.net/1974/14633.

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

MLA Handbook (7^th Edition):

Beheshti Vadeqan, Babak. “Geometry of Dirac Operators .” 2016. Web. 25 Jan 2021.

Vancouver:

Beheshti Vadeqan B. Geometry of Dirac Operators . [Internet] [Thesis]. Queens University; 2016. [cited 2021 Jan 25]. Available from: http://hdl.handle.net/1974/14633.

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

Council of Science Editors:

Beheshti Vadeqan B. Geometry of Dirac Operators . [Thesis]. Queens University; 2016. Available from: http://hdl.handle.net/1974/14633

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

Université de Bordeaux I

8. Sambou, Diomba. Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians.

Degree: Docteur es, Mathématiques appliquées et calcul scientifique, 2013, Université de Bordeaux I

URL: http://www.theses.fr/2013BOR14906

►

Dans cette thèse on s'interesse à l'étude de phénomènes d'accumultation spectrale de certains opérateurs issus de la physique quantique à savoir les opérateurs de Schrödinger,… (more)

▼

Dans cette thèse on s'interesse à l'étude de phénomènes d'accumultation spectrale de certains opérateurs issus de la physique quantique à savoir les opérateurs de Schrödinger, de Pauli, et de Dirac. Typiquement, ces opérateurs apparaissent dans la modélisation de certains problèmes de physique sous forme d'équations d'évolution. Selon les contraintes du problème physique, ils peuvent être associés ou non à un champ magnétique pouvant être constant ou non constant. Le cadre où le champ magnétique est dit admissible est celui que nous allons considérer (en dimension 3). Ce dernier cadre inclut en particulier le cas de champs magnétiques constants. Deux grands thèmes sont essentiellement abordés dans cette thèse : l'étude des résonances près de seuils des Hamiltoniens quantiques cités ci-dessus lorsqu'ils sont perturbés par des potentiels électriques auto-adjoints, et l'étude de leur spectre discret lorsqu'ils sont perturbés par des potentiels électriques non auto-adjoints. Le second thème sera exploré au moyent d'inégalités Lieb-Thirring généralisés.

In this thesis we are interested to the study of spectral accumulation phenomena of some opeators coming from quantum physics, namely Schrödinger, Paul and Dirac operators. Typically, these operators appear in the modeling of some physical problems in the form of evolution equations. According to the constraints of the physical problem, they can be associated or not to a constant or non constant magnetic field. The contextt where the magnetic field is admissible is that we shall consider (in dimention 3). This framework includes in particular the case of constant magnetic fields. Essentieally, two main themes are discussed in this thesis : the study of resonances near thescholds of the quantum Hamiltonians mentioned above perturbed by self-adjoint potentials, and the study of their discrete spectrum when thy are perturbed by non self-adjoint potentials. The second theme will be investigated with the help of generalized Lieb-Thirring inequalities.

Advisors/Committee Members: Bruneau, Vincent (thesis director), Kupin, Stanislas (thesis director).

Subjects/Keywords: Opérateurs de Schrödinger; Opérateurs de Pauli; Opérateurs de Dirac magnétiques,; Résonances; Inégalités Lieb-Thirring généralisées.; Magnetic Schrödinger; Dirac operators; Pauli operatoirs; Resonances; Generalized Lieb-Thirring inequalities

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APA (6^th Edition):

Sambou, D. (2013). Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians. (Doctoral Dissertation). Université de Bordeaux I. Retrieved from http://www.theses.fr/2013BOR14906

Chicago Manual of Style (16^th Edition):

Sambou, Diomba. “Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians.” 2013. Doctoral Dissertation, Université de Bordeaux I. Accessed January 25, 2021. http://www.theses.fr/2013BOR14906.

MLA Handbook (7^th Edition):

Sambou, Diomba. “Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians.” 2013. Web. 25 Jan 2021.

Vancouver:

Sambou D. Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians. [Internet] [Doctoral dissertation]. Université de Bordeaux I; 2013. [cited 2021 Jan 25]. Available from: http://www.theses.fr/2013BOR14906.

Council of Science Editors:

Sambou D. Accumulation spectrale pour les Hamiltoniens quantiques magnétiques : Spectral accumulation for magnetic quantum Hamiltonians. [Doctoral Dissertation]. Université de Bordeaux I; 2013. Available from: http://www.theses.fr/2013BOR14906

9. Klaasse, R.L. Seiberg-Witten theory for symplectic manifolds.

Degree: 2013, Universiteit Utrecht

URL: http://dspace.library.uu.nl:8080/handle/1874/282753

► In this thesis we give an introduction to Seiberg-Witten gauge theory used to study compact oriented four-dimensional manifolds X. Seiberg-Witten theory uses a Spin c… (more)

Subjects/Keywords: Seiberg-Witten theory; four-manifolds; symplectic manifolds; Spin c structures; Dirac operators

…forms, so that we are done. 2.4 Elliptic operators In this section we discuss the notion of… …analogous notion for operators between sections of vector bundles. Definition 2.4.2. An operator D… …of Fredholm operators is that their index is invariant under perturbations. In other words… …if one were to take a family of Fredholm operators parameterized by some connected… …Fredholmness of operators and calculating their index. A key concept is that of ellipticity. Let π…

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APA (6^th Edition):

Klaasse, R. L. (2013). Seiberg-Witten theory for symplectic manifolds. (Masters Thesis). Universiteit Utrecht. Retrieved from http://dspace.library.uu.nl:8080/handle/1874/282753

Chicago Manual of Style (16^th Edition):

Klaasse, R L. “Seiberg-Witten theory for symplectic manifolds.” 2013. Masters Thesis, Universiteit Utrecht. Accessed January 25, 2021. http://dspace.library.uu.nl:8080/handle/1874/282753.

MLA Handbook (7^th Edition):

Klaasse, R L. “Seiberg-Witten theory for symplectic manifolds.” 2013. Web. 25 Jan 2021.

Vancouver:

Klaasse RL. Seiberg-Witten theory for symplectic manifolds. [Internet] [Masters thesis]. Universiteit Utrecht; 2013. [cited 2021 Jan 25]. Available from: http://dspace.library.uu.nl:8080/handle/1874/282753.

Council of Science Editors:

Klaasse RL. Seiberg-Witten theory for symplectic manifolds. [Masters Thesis]. Universiteit Utrecht; 2013. Available from: http://dspace.library.uu.nl:8080/handle/1874/282753

10. Lal, Nishu. Spectral Zeta Functions of Laplacians on Self-Similar Fractals.

Degree: Mathematics, 2012, University of California – Riverside

URL: http://www.escholarship.org/uc/item/888903d2

► This thesis investigates the spectral zeta function of fractal differential operators such as the Laplacian on the unbounded (i.e., infinite) Sierpinski gasket and a self-similar… (more)

Subjects/Keywords: Mathematics; Analysis on fractals; decimation method; Dirac delta hyperfunction; fractal Sturm-Liouville operators; multivariable complex dynamics; spectral zeta functions

…the spectral zeta function of fractal differential operators such as the Laplacian on the… …the spectral zeta function of such an operator, expressed in terms of the Dirac delta… …variables associated with fractal Sturm–Liouville operators. Moreover, as a corollary, in the very… …Adjoint Operators and Quadratic Forms . . . . . . 2.5 Introduction To Hyperfunctions… …3.3.1 Main Lemma Regarding the Dirac Delta Hyperfunction . . . . . 3.4 A Representation of the…

5 more images…

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APA (6^th Edition):

Lal, N. (2012). Spectral Zeta Functions of Laplacians on Self-Similar Fractals. (Thesis). University of California – Riverside. Retrieved from http://www.escholarship.org/uc/item/888903d2

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):

Lal, Nishu. “Spectral Zeta Functions of Laplacians on Self-Similar Fractals.” 2012. Thesis, University of California – Riverside. Accessed January 25, 2021. http://www.escholarship.org/uc/item/888903d2.

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

MLA Handbook (7^th Edition):

Lal, Nishu. “Spectral Zeta Functions of Laplacians on Self-Similar Fractals.” 2012. Web. 25 Jan 2021.

Vancouver:

Lal N. Spectral Zeta Functions of Laplacians on Self-Similar Fractals. [Internet] [Thesis]. University of California – Riverside; 2012. [cited 2021 Jan 25]. Available from: http://www.escholarship.org/uc/item/888903d2.

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

Council of Science Editors:

Lal N. Spectral Zeta Functions of Laplacians on Self-Similar Fractals. [Thesis]. University of California – Riverside; 2012. Available from: http://www.escholarship.org/uc/item/888903d2

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

11. Reynolds, Paul. On conformal submersions and manifolds with exceptional structure groups.

Degree: PhD, 2012, University of Edinburgh

URL: http://hdl.handle.net/1842/6218

► This thesis comes in three main parts. In the first of these (comprising chapters 2 - 6), the basic theory of Riemannian and conformal submersions… (more)

Subjects/Keywords: 519; Riemannian submersions; conformal submersions; Clifford algebra; spinor bundles; Dirac operators; quaternionic-Kahler quotients

…56 6 Dirac Operators and Conformal 6.1 Dirac operator formulae . . . . 6.2 One-dimensional… …distribution V The mean curvature of the horizontal distribution H Various Dirac operators The real… …next step is to calculate expressions for the Dirac operators. This does not require us to… …on M constructed from these. The Dirac operators of the total space, base and fibres are… …Calculation of the Dirac operators and application to the characterisation of Dirac morphisms. 8…

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APA (6^th Edition):

Reynolds, P. (2012). On conformal submersions and manifolds with exceptional structure groups. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/6218

Chicago Manual of Style (16^th Edition):

Reynolds, Paul. “On conformal submersions and manifolds with exceptional structure groups.” 2012. Doctoral Dissertation, University of Edinburgh. Accessed January 25, 2021. http://hdl.handle.net/1842/6218.

MLA Handbook (7^th Edition):

Reynolds, Paul. “On conformal submersions and manifolds with exceptional structure groups.” 2012. Web. 25 Jan 2021.

Vancouver:

Reynolds P. On conformal submersions and manifolds with exceptional structure groups. [Internet] [Doctoral dissertation]. University of Edinburgh; 2012. [cited 2021 Jan 25]. Available from: http://hdl.handle.net/1842/6218.

Council of Science Editors:

Reynolds P. On conformal submersions and manifolds with exceptional structure groups. [Doctoral Dissertation]. University of Edinburgh; 2012. Available from: http://hdl.handle.net/1842/6218

University of Michigan

12. Korpas, Levente. Quantization of symplectic cobordisms.

Degree: PhD, Pure Sciences, 1999, University of Michigan

URL: http://hdl.handle.net/2027.42/131922

► In this work we construct a unitary operator acting between Spin^c quantizations of compact integral symplectic manifolds which are symplectically cobordant. The construction is… (more)

Subjects/Keywords: Cobordisms; Dirac Operators; Quantization; Symplectic Manifolds

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APA (6^th Edition):

Korpas, L. (1999). Quantization of symplectic cobordisms. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/131922

Chicago Manual of Style (16^th Edition):

Korpas, Levente. “Quantization of symplectic cobordisms.” 1999. Doctoral Dissertation, University of Michigan. Accessed January 25, 2021. http://hdl.handle.net/2027.42/131922.

MLA Handbook (7^th Edition):

Korpas, Levente. “Quantization of symplectic cobordisms.” 1999. Web. 25 Jan 2021.

Vancouver:

Korpas L. Quantization of symplectic cobordisms. [Internet] [Doctoral dissertation]. University of Michigan; 1999. [cited 2021 Jan 25]. Available from: http://hdl.handle.net/2027.42/131922.

Council of Science Editors:

Korpas L. Quantization of symplectic cobordisms. [Doctoral Dissertation]. University of Michigan; 1999. Available from: http://hdl.handle.net/2027.42/131922

University of Michigan

13. Sandoval, Mary Ruth. Wave-trace asymptotics for operators of Dirac type.

Degree: PhD, Pure Sciences, 1997, University of Michigan

URL: http://hdl.handle.net/2027.42/130578

► Spectral geometry seeks to understand the relationship between the spectra of differential operators and the underlying geometry of a manifold, especially to understand which geometric… (more)

Subjects/Keywords: Asymptotics; Dirac; Operators; Spectral Geometry; Trace; Type; Wave

Record Details Similar Records Cite « Share

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

APA (6^th Edition):

Sandoval, M. R. (1997). Wave-trace asymptotics for operators of Dirac type. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/130578

Chicago Manual of Style (16^th Edition):

Sandoval, Mary Ruth. “Wave-trace asymptotics for operators of Dirac type.” 1997. Doctoral Dissertation, University of Michigan. Accessed January 25, 2021. http://hdl.handle.net/2027.42/130578.

MLA Handbook (7^th Edition):

Sandoval, Mary Ruth. “Wave-trace asymptotics for operators of Dirac type.” 1997. Web. 25 Jan 2021.

Vancouver:

Sandoval MR. Wave-trace asymptotics for operators of Dirac type. [Internet] [Doctoral dissertation]. University of Michigan; 1997. [cited 2021 Jan 25]. Available from: http://hdl.handle.net/2027.42/130578.

Council of Science Editors:

Sandoval MR. Wave-trace asymptotics for operators of Dirac type. [Doctoral Dissertation]. University of Michigan; 1997. Available from: http://hdl.handle.net/2027.42/130578

University of Waterloo

14. Suan, Caleb. Differential Operators on Manifolds with G2-Structure.

Degree: 2020, University of Waterloo

URL: http://hdl.handle.net/10012/16565

► In this thesis, we study differential operators on manifolds with torsion-free G2-structure. In particular, we use an identification of the spinor bundle S of such… (more)

Subjects/Keywords: differential geometry; G2-structures; twisted Dirac operator; differential operators

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

APA (6^th Edition):

Suan, C. (2020). Differential Operators on Manifolds with G2-Structure. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/16565

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):

Suan, Caleb. “Differential Operators on Manifolds with G2-Structure.” 2020. Thesis, University of Waterloo. Accessed January 25, 2021. http://hdl.handle.net/10012/16565.

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

MLA Handbook (7^th Edition):

Suan, Caleb. “Differential Operators on Manifolds with G2-Structure.” 2020. Web. 25 Jan 2021.

Vancouver:

Suan C. Differential Operators on Manifolds with G2-Structure. [Internet] [Thesis]. University of Waterloo; 2020. [cited 2021 Jan 25]. Available from: http://hdl.handle.net/10012/16565.

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

Council of Science Editors:

Suan C. Differential Operators on Manifolds with G2-Structure. [Thesis]. University of Waterloo; 2020. Available from: http://hdl.handle.net/10012/16565

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

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Open Access Theses and Dissertations