Commutative and Noncommutative Harmonic Analysis and Applications.

Intro -- Preface -- Remembering Daryl Geller (1950 - 2011) -- Publications -- List of speakers -- List of participants -- Part I [.3cm] Noncommutative Harmonic Analysis -- Krein-Space Operators Induced by Dirichlet Characters -- 1. Introduction -- 2. Preliminaries -- 3. Free Probabilistic Model of Induced by Primes -- 4. Dirichlet Character Subsets of -- 5. Free Distributional Data of Dirichlet Characters -- 6. Representations of the Arithmetic Algebra -- 7. Krein-Space Operators Induced by Dirichlet Characters on \frak{ }_{ } -- 8. Krein-Space Operator Induced by Dirichlet Characters on ℂ_{ ₒ}² -- References -- Noncommutative solenoids and their projective modules -- 1. Introduction -- 2. Noncommutative Solenoids -- 3. Classification of the noncommutative Solenoids -- 4. Forming projective modules over noncommutative solenoids from the inside out -- 5. Forming projective modules over noncommutative solenoids using -adic fields -- References -- Paley-Wiener-Schwartz nearly Parseval frames on noncompact symmetric spaces -- 1. Introduction -- 2. Harmonic analysis on Riemannian symmetric spaces of the noncompact type -- 3. Paley-Wiener spaces _{ }( ) -- 4. Average sampling and almost Parseval frames in Paley-Wiener spaces on Riemannian manifolds -- 5. Nearly Parseval Paley-Wiener frames on = / -- References -- Projective multiresolution analyses over irrational rotation algebras -- 1. Introduction -- 2. Preliminaries -- 3. Definition of projective multiresolution analysis -- 4. A PMRA over _{ } that is initially free -- 5. Building the module frame -- 6. Conclusion and open questions -- References -- Part II [.3cm]Commutative Harmonic Analysis -- Regularity of abelian linear actions -- 1. Introduction -- 2. Analytic group actions and regular orbits -- 3. Group action on a fiber bundle.

4. Linear action of a connected abelian group -- References -- -widths and approximation theory on compact Riemannian manifolds -- 1. Introduction and main results -- 2. Kernels of elliptic operators on compact Riemannian manifolds -- 3. Proof of Theorem 1.1 -- 4. Widths of balls in Besov spaces -- 5. Approximation theory on compact homogeneous manifolds -- References -- A four dimensional continuous wavelet transform -- 1. Introduction -- 2. The four dimensional transform -- 3. Notation and definitions -- 4. A square-integrable irreducible representation -- 5. The general continuous wavelet transform -- 6. A discrete frame -- References -- Part III Applications -- Dynamical Sampling in Shift-Invariant Spaces -- 1. Introduction -- 2. Dynamical Sampling in Shift-Invariant Spaces -- References -- High-Frequency Tail Index Estimation by Nearly Tight Frames -- 1. Introduction -- 2. Random fields and mexican needlets -- 3. Mexican Needlet Whittle-like approximation to likelihood function -- 4. Asymptotic Properties -- 5. Narrow band estimates -- 6. The Plug-in procedure -- Appendix A. Auxiliary results: preliminaries -- Appendix B. Auxiliary Results: Covariance terms -- Appendix C. Auxiliary Results: Cumulants -- References -- Multiplexing and demultiplexing Frame Pairs -- 1. Introduction and statement of main results -- 2. Preliminaries and definitions -- 3. Multiplexing and demultiplexing pairs -- 4. Example -- 5. Appendix -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.