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 𝒜 Induced by Primes

4. Dirichlet Character Subsets of 𝒜

5. Free Distributional Data of Dirichlet Characters

6. Representations of the Arithmetic Algebra

7. Krein-Space Operators Induced by Dirichlet Characters on \frak{𝐾}_{𝑝}

8. Krein-Space Operator Induced by Dirichlet Characters on ℂ_{𝔸ₒ}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 𝑝-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 𝑃𝑊_{𝜔}(𝑋)

4. Average sampling and almost Parseval frames in Paley-Wiener spaces on Riemannian manifolds

5. Nearly Parseval Paley-Wiener frames on 𝑋=𝐺/𝐾

References

Projective multiresolution analyses over irrational rotation algebras

1. Introduction

2. Preliminaries

3. Definition of projective multiresolution analysis

4. A PMRA over 𝐴_{𝛼} 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

𝑛-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