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University of Illinois – Urbana-Champaign

1. Zeng, Qiang. Poincar�� inequalities in noncommutative Lp spaces.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/50527

► Let (\mathcal{N},τ) be a noncommutative W^* probability space, where \mathcal{N} is a finite von Neumann algebra and τ is a normal faithful tracial state. Let…
(more)

Subjects/Keywords: noncommutative Lp spaces; Poincaré inequalities; $\Gamma_2$-criterion; martingale inequalities; Burkholder inequality; spectral gap; diffusion semigroups; transportation cost inequalities; law of the iterated logarithm; subgaussian concentration; 1-cocycle on groups; finite von Neumann algebras

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APA (6^{th} Edition):

Zeng, Q. (2014). Poincar�� inequalities in noncommutative Lp spaces. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/50527

Chicago Manual of Style (16^{th} Edition):

Zeng, Qiang. “Poincar�� inequalities in noncommutative Lp spaces.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/50527.

MLA Handbook (7^{th} Edition):

Zeng, Qiang. “Poincar�� inequalities in noncommutative Lp spaces.” 2014. Web. 05 Jun 2020.

Vancouver:

Zeng Q. Poincar�� inequalities in noncommutative Lp spaces. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/50527.

Council of Science Editors:

Zeng Q. Poincar�� inequalities in noncommutative Lp spaces. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/50527

University of Illinois – Urbana-Champaign

2. Demirbas, Seckin. A study on certain periodic Schrödinger equations.

Degree: PhD, Mathematics, 2015, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/87978

In the first part of this thesis we consider the cubic Schrödinger equation
iu_{t+Delta} u =+/-|u|^{2u}, x in T_{theta}^{2}, t∈ [-T,T],
u(x,0)=u_{0}(x) in H^{s}(T_{theta}^{2}).
T is the time of existence of the solutions and T_{theta}^{2} is the irrational torus given by R^{2}/theta_{1} Z * θ_{2} Z for theta_{1}, theta_{2} > 0 and theta_{1}/theta_{2} irrational. Our main result is an improvement of the Strichartz estimates on irrational tori using a counting argument by Huxley [43], which estimates the number of lattice points on ellipsoids. With this Strichartz estimate, we obtain a local well-posedness result in H^{s} for s>131/416. We also use energy type estimates to control the H^{s} norm of the solution and obtain improved growth bounds for higher order Sobolev norms.
In the second and the third parts of this thesis, we study the Cauchy problem for the 1d periodic fractional Schrödinger equation:
iu_{t+}(-Delta)^{alpha} u =+/- |u|^{2u}, x in T, t in R,
u(x,0)=u_{0}(x) in H^{s}(T),
where alpha in (1/2,1). First, we prove a Strichartz type estimate for this equation. Using the arguments from Chapter 3, this estimate implies local well-posedness in H^{s} for s>(1-alpha)/2. However, we prove local well-posedness using direct X^(s,b) estimates. In addition, we show the existence of global-in-time infinite energy solutions. We also show that the nonlinear evolution of the equation is smoother than the initial data. As an important consequence of this smoothing estimate, we prove that there is global well-posedness in H^{s} for s>(10*alpha+1)/(12).
Finally, for the fractional Schrödinger equation, we define an invariant probability measure mu on H^{s} for s<alpha-1/2, called a Gibbs measure. We define mu so that for any epsilon>0 there is a set Omega, a subset of H^{s}, such that mu(Omega^{c})<epsilon and the equation is globally well-posed for initial data in Omega. We achieve this by showing that for the initial data in Omega, the H^{s} norms of the solutions stay finite for all times. This fills the gap between the local well-posedness and the global well-posedness range in almost sure sense for (1-alpha)/2<alpha-1/2, i.e. alpha>2/3.
*Advisors/Committee Members: Tzirakis, Nikolaos (advisor), Erdogan, Burak (advisor), Junge, Marius (Committee Chair), Bronski, Jared C. (committee member).*

Subjects/Keywords: Periodic Schrodinger equation; Fractional Schrodinger equation

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

APA (6^{th} Edition):

Demirbas, S. (2015). A study on certain periodic Schrödinger equations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/87978

Chicago Manual of Style (16^{th} Edition):

Demirbas, Seckin. “A study on certain periodic Schrödinger equations.” 2015. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/87978.

MLA Handbook (7^{th} Edition):

Demirbas, Seckin. “A study on certain periodic Schrödinger equations.” 2015. Web. 05 Jun 2020.

Vancouver:

Demirbas S. A study on certain periodic Schrödinger equations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2015. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/87978.

Council of Science Editors:

Demirbas S. A study on certain periodic Schrödinger equations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/87978

University of Illinois – Urbana-Champaign

3. Rezvani, Sepideh. Approximating rotation algebras and inclusions of C*-algebras.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/97307

► In the first part of this thesis, we will follow Kirchberg’s categorical perspective to establish new notions of WEP and QWEP relative to a C∗-algebra,…
(more)

Subjects/Keywords: C*-algebras; Weak expectation property (WEP); Quotient weak expectation property (QWEP); A-WEP; A-QWEP; Relatively weak injectivity; Order-unit space; Noncommutative tori; Compact quantum metric space; Conditionally negative length function; Heat semigroup; Poisson semigroup; Rotation algebra; Continuous field of compact quantum metric spaces; Gromov–Hausdorff distance; Completely bounded quantum Gromov–Hausdorff distance; Gromov–Hausdorff propinquity

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

APA (6^{th} Edition):

Rezvani, S. (2017). Approximating rotation algebras and inclusions of C*-algebras. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/97307

Chicago Manual of Style (16^{th} Edition):

Rezvani, Sepideh. “Approximating rotation algebras and inclusions of C*-algebras.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/97307.

MLA Handbook (7^{th} Edition):

Rezvani, Sepideh. “Approximating rotation algebras and inclusions of C*-algebras.” 2017. Web. 05 Jun 2020.

Vancouver:

Rezvani S. Approximating rotation algebras and inclusions of C*-algebras. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/97307.

Council of Science Editors:

Rezvani S. Approximating rotation algebras and inclusions of C*-algebras. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/97307

University of Illinois – Urbana-Champaign

4. Compaan, Erin Leigh. Smoothing properties of certain dispersive nonlinear partial differential equations.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/97315

► This thesis is primarily concerned with the smoothing properties of dispersive equations and systems. Smoothing in this context means that the nonlinear part of the…
(more)

Subjects/Keywords: Dispersive partial differential equations; Well-posedness; Smoothing; Zakharov; Klein-Gordon Schrödinger; Majda-Biello; Boussinesq equation

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APA (6^{th} Edition):

Compaan, E. L. (2017). Smoothing properties of certain dispersive nonlinear partial differential equations. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/97315

Chicago Manual of Style (16^{th} Edition):

Compaan, Erin Leigh. “Smoothing properties of certain dispersive nonlinear partial differential equations.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/97315.

MLA Handbook (7^{th} Edition):

Compaan, Erin Leigh. “Smoothing properties of certain dispersive nonlinear partial differential equations.” 2017. Web. 05 Jun 2020.

Vancouver:

Compaan EL. Smoothing properties of certain dispersive nonlinear partial differential equations. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/97315.

Council of Science Editors:

Compaan EL. Smoothing properties of certain dispersive nonlinear partial differential equations. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/97315

University of Illinois – Urbana-Champaign

5. Albar, Wafaa Abdullah. Non commutative version of arithmetic geometric mean inequality and crossed product of ternary ring of operators.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98206

► This thesis is structured into two parts. In the first two chapters, we prove the non commutative version of the Arithmetic Geometric Mean (AGM) inequality…
(more)

Subjects/Keywords: Arithmetic geometric mean inequality (AGM); Random matrices; Ternary ring of operators (TRO); Crossed product of ternary ring of operators (TROs)

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APA (6^{th} Edition):

Albar, W. A. (2017). Non commutative version of arithmetic geometric mean inequality and crossed product of ternary ring of operators. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98206

Chicago Manual of Style (16^{th} Edition):

Albar, Wafaa Abdullah. “Non commutative version of arithmetic geometric mean inequality and crossed product of ternary ring of operators.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/98206.

MLA Handbook (7^{th} Edition):

Albar, Wafaa Abdullah. “Non commutative version of arithmetic geometric mean inequality and crossed product of ternary ring of operators.” 2017. Web. 05 Jun 2020.

Vancouver:

Albar WA. Non commutative version of arithmetic geometric mean inequality and crossed product of ternary ring of operators. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/98206.

Council of Science Editors:

Albar WA. Non commutative version of arithmetic geometric mean inequality and crossed product of ternary ring of operators. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98206

University of Illinois – Urbana-Champaign

6. Percel, Ian M. A quantum measurement model of reaction-transport systems.

Degree: PhD, Nuclear Engineering, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/100918

► This research develops a mesoscopic quantum measurement theoretic foundation for neutron transport theory in the presence of delayed fission and compound scattering processes. Specifically, we…
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Subjects/Keywords: Quantum Measurement; Quantum Probability; Quantum Stochastic Processes; Transport Theory; Neutron Thermalization

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

APA (6^{th} Edition):

Percel, I. M. (2018). A quantum measurement model of reaction-transport systems. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/100918

Chicago Manual of Style (16^{th} Edition):

Percel, Ian M. “A quantum measurement model of reaction-transport systems.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/100918.

MLA Handbook (7^{th} Edition):

Percel, Ian M. “A quantum measurement model of reaction-transport systems.” 2018. Web. 05 Jun 2020.

Vancouver:

Percel IM. A quantum measurement model of reaction-transport systems. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/100918.

Council of Science Editors:

Percel IM. A quantum measurement model of reaction-transport systems. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/100918

7. Avsec, Stephen. Gaussian-like von Neumann algebras and noncommutative brownian motion.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34412

► The q-Gaussian von Neumann algebras were first defined and studied by Bo\.{z}ejko and Speicher in connection with noncommutative brownian motion. The main results of the…
(more)

Subjects/Keywords: noncommutative probability; von Neumann algebras

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APA (6^{th} Edition):

Avsec, S. (2012). Gaussian-like von Neumann algebras and noncommutative brownian motion. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34412

Chicago Manual of Style (16^{th} Edition):

Avsec, Stephen. “Gaussian-like von Neumann algebras and noncommutative brownian motion.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/34412.

MLA Handbook (7^{th} Edition):

Avsec, Stephen. “Gaussian-like von Neumann algebras and noncommutative brownian motion.” 2012. Web. 05 Jun 2020.

Vancouver:

Avsec S. Gaussian-like von Neumann algebras and noncommutative brownian motion. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/34412.

Council of Science Editors:

Avsec S. Gaussian-like von Neumann algebras and noncommutative brownian motion. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34412

8. Zhao, Mingyu. Smoothing estimates for non commutative spaces.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101570

► In the first part of this thesis, we follow Varopoulos's perspective to establish the noncommutaive Sobolev inequaties (namely, Hardy-Littlewood-Sobolev inequalites), and extend the Sobolev embedding…
(more)

Subjects/Keywords: harmonic analysis; Hardy-Littlewood-Sobolev inequalities; Functional analysis; Operator space; Operator algebras; non-commutaive $L_p$ spaces

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

APA (6^{th} Edition):

Zhao, M. (2018). Smoothing estimates for non commutative spaces. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101570

Chicago Manual of Style (16^{th} Edition):

Zhao, Mingyu. “Smoothing estimates for non commutative spaces.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/101570.

MLA Handbook (7^{th} Edition):

Zhao, Mingyu. “Smoothing estimates for non commutative spaces.” 2018. Web. 05 Jun 2020.

Vancouver:

Zhao M. Smoothing estimates for non commutative spaces. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/101570.

Council of Science Editors:

Zhao M. Smoothing estimates for non commutative spaces. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101570

9. Gao, Li. On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101546

► Quantum Euclidean spaces are noncommutative deformations of Euclidean spaces. They are prototypes of locally compact noncommutative manifolds in Noncommutative Geometry. In this thesis, we study…
(more)

Subjects/Keywords: Noncommutative Euclidean spaces; Moyal Deformation; Pseudo-differential operators

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APA (6^{th} Edition):

Gao, L. (2018). On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101546

Chicago Manual of Style (16^{th} Edition):

Gao, Li. “On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/101546.

MLA Handbook (7^{th} Edition):

Gao, Li. “On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators.” 2018. Web. 05 Jun 2020.

Vancouver:

Gao L. On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/101546.

Council of Science Editors:

Gao L. On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101546

10. Liang, Jian. Operator-valued Kirchberg Theory and its connection to tensor norms and correspondences.

Degree: PhD, Mathematics, 2015, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/78377

► In this thesis, we will first follow Kirchberg’s categorical perspective to establish operator-valued WEP and QWEP. We develop similar properties as that in the classical…
(more)

Subjects/Keywords: Kirchberg; Module

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APA (6^{th} Edition):

Liang, J. (2015). Operator-valued Kirchberg Theory and its connection to tensor norms and correspondences. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/78377

Chicago Manual of Style (16^{th} Edition):

Liang, Jian. “Operator-valued Kirchberg Theory and its connection to tensor norms and correspondences.” 2015. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/78377.

MLA Handbook (7^{th} Edition):

Liang, Jian. “Operator-valued Kirchberg Theory and its connection to tensor norms and correspondences.” 2015. Web. 05 Jun 2020.

Vancouver:

Liang J. Operator-valued Kirchberg Theory and its connection to tensor norms and correspondences. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2015. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/78377.

Council of Science Editors:

Liang J. Operator-valued Kirchberg Theory and its connection to tensor norms and correspondences. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2015. Available from: http://hdl.handle.net/2142/78377

11. Miller, Jesse E. Nonstandard techniques in lifting theory.

Degree: PhD, 0439, 2011, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/24411

► In this dissertation, a nonstandard approach to lifting theory developed by Bliedtner and Loeb is applied to liftings on topological measure spaces and group measure…
(more)

Subjects/Keywords: lifting; measure; nonstandard analysis

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APA (6^{th} Edition):

Miller, J. E. (2011). Nonstandard techniques in lifting theory. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/24411

Chicago Manual of Style (16^{th} Edition):

Miller, Jesse E. “Nonstandard techniques in lifting theory.” 2011. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/24411.

MLA Handbook (7^{th} Edition):

Miller, Jesse E. “Nonstandard techniques in lifting theory.” 2011. Web. 05 Jun 2020.

Vancouver:

Miller JE. Nonstandard techniques in lifting theory. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2011. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/24411.

Council of Science Editors:

Miller JE. Nonstandard techniques in lifting theory. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2011. Available from: http://hdl.handle.net/2142/24411

12. Lee, Kiryung. Efficient and guaranteed algorithms for sparse inverse problems.

Degree: PhD, 1200, 2012, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/34346

► Compressed sensing is a new data acquisition paradigm enabling universal, simple, and reduced-cost acquisition, by exploiting a sparse signal model. Most notably, recovery of the…
(more)

Subjects/Keywords: compressed sensing; oblique projection; restricted isometry property (RIP); random matrices; joint sparsity; multiple measurement vectors (MMV); sensor array processing; spectrum-blind sampling; subspace estimation; matrix completion; performance guarantee; rank minimization

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

APA (6^{th} Edition):

Lee, K. (2012). Efficient and guaranteed algorithms for sparse inverse problems. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/34346

Chicago Manual of Style (16^{th} Edition):

Lee, Kiryung. “Efficient and guaranteed algorithms for sparse inverse problems.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/34346.

MLA Handbook (7^{th} Edition):

Lee, Kiryung. “Efficient and guaranteed algorithms for sparse inverse problems.” 2012. Web. 05 Jun 2020.

Vancouver:

Lee K. Efficient and guaranteed algorithms for sparse inverse problems. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/34346.

Council of Science Editors:

Lee K. Efficient and guaranteed algorithms for sparse inverse problems. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: http://hdl.handle.net/2142/34346

University of Illinois – Urbana-Champaign

13. Lee, Jung Jin. On p-operator spaces and their applications.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/16714

► There have been a lot of research done on the relationship between locally compact groups and algebras associated with them. For example, Johnson proved that…
(more)

Subjects/Keywords: p-operator space; pseudofunction algebra; pseudomeasure algebra; Figa-Talamanca-Herz algebra

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

APA (6^{th} Edition):

Lee, J. J. (2010). On p-operator spaces and their applications. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16714

Chicago Manual of Style (16^{th} Edition):

Lee, Jung Jin. “On p-operator spaces and their applications.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/16714.

MLA Handbook (7^{th} Edition):

Lee, Jung Jin. “On p-operator spaces and their applications.” 2010. Web. 05 Jun 2020.

Vancouver:

Lee JJ. On p-operator spaces and their applications. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/16714.

Council of Science Editors:

Lee JJ. On p-operator spaces and their applications. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16714

University of Illinois – Urbana-Champaign

14. Cooney, Thomas J. Noncommutative Lp-spaces associated with locally compact quantum groups.

Degree: PhD, 0439, 2010, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/16895

► Results from abstract harmonic analysis are extended to locally compact quantum groups by considering the noncommutative Lp-spaces associated with the locally compact quantum groups. Let…
(more)

Subjects/Keywords: Locally compact quantum groups; Noncommutative Lp-spaces; Noncommutative harmonic analysis; Fourier transform; Fourier multipliers; Hausdorff-Young inequality

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APA (6^{th} Edition):

Cooney, T. J. (2010). Noncommutative Lp-spaces associated with locally compact quantum groups. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/16895

Chicago Manual of Style (16^{th} Edition):

Cooney, Thomas J. “Noncommutative Lp-spaces associated with locally compact quantum groups.” 2010. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed June 05, 2020. http://hdl.handle.net/2142/16895.

MLA Handbook (7^{th} Edition):

Cooney, Thomas J. “Noncommutative Lp-spaces associated with locally compact quantum groups.” 2010. Web. 05 Jun 2020.

Vancouver:

Cooney TJ. Noncommutative Lp-spaces associated with locally compact quantum groups. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2010. [cited 2020 Jun 05]. Available from: http://hdl.handle.net/2142/16895.

Council of Science Editors:

Cooney TJ. Noncommutative Lp-spaces associated with locally compact quantum groups. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2010. Available from: http://hdl.handle.net/2142/16895