**Contemporary Mathematics**

Volume: 650;
2015;
209 pp;
Softcover

MSC: Primary 22; 32; 42; 46; 41; 43;

Print ISBN: 978-1-4704-1879-3

Product Code: CONM/650

List Price: $105.00

AMS Member Price: $84.00

MAA Member Price: $94.50

**Electronic ISBN: 978-1-4704-2777-1
Product Code: CONM/650.E**

List Price: $105.00

AMS Member Price: $84.00

MAA Member Price: $94.50

# Trends in Harmonic Analysis and Its Applications

Share this page *Edited by *
*Jens G. Christensen; Susanna Dann; Azita Mayeli; Gestur Ólafsson*

This volume contains the proceedings of the
AMS Special Session on Harmonic Analysis and Its Applications, held
March 29–30, 2014, at the University of Maryland, Baltimore County,
Baltimore, MD.

It provides an in depth look at the many directions taken by
experts in Harmonic Analysis and related areas. The papers cover
topics such as frame theory, Gabor analysis, interpolation and Besov
spaces on compact manifolds, Cuntz-Krieger algebras, reproducing
kernel spaces, solenoids, hypergeometric shift operators and analysis
on infinite dimensional groups.

Expositions are by leading researchers in the field, both young and
established. The papers consist of new results or new approaches to
solutions, and at the same time provide an introduction into the
respective subjects.

#### Readership

Graduate students and research mathematicians interested in harmonic analysis, frame theory, and functional analysis.

# Table of Contents

## Trends in Harmonic Analysis and Its Applications

- Cover Cover11 free
- Title page i2 free
- Contents iii4 free
- Chapter 1. Preface v6 free
- Frame Theory 18 free
- Phase retrieval and norm retrieval 310
- On Lipschitz inversion of nonlinear redundant representations 1522
- Tight and random nonorthogonal fusion frames 2330
- Decompositions of rational Gabor representations 3744
- Functional Analysis and 𝐶*-algebras 5562
- Representations of Cuntz-Krieger relations, dynamics on Bratteli diagrams, and path-space measures 5764
- A survey of amenability theory for direct-limit groups 8996
- 1. Introduction 8996
- 2. Means on Topological Groups 9198
- 3. Amenable Groups 94101
- 4. Unitarizability 96103
- 5. Invariant Means and Regular Representations 98105
- 6. Almost Periodic Functions 100107
- 7. Direct Limits of Abelian Groups 101108
- 8. Spherical Functions and Direct Limits 102109
- References 108115

- Explicit construction of equivalence bimodules between noncommutative solenoids 111118
- 1. Introduction 111118
- 2. Review of the construction of noncommutative solenoids 113120
- 3. Directed systems of equivalence bimodules: a method to form equivalence bimodules between direct limits of 𝐶*-algebras 115122
- 4. The explicit construction of equivalence bimodules at each stage 119126
- 5. Forming projective modules over noncommutative solenoids using 𝑝-adic fields 123130
- 6. The Haar multiresolution analysis for 𝐿²(ℚ_{𝕡}) of Shelkovich and Skopina 126133
- 7. The Haar MRS for 𝐿²(ℚ_{𝕡}) and projective multiresolution structures 129136
- References 139146

- Harmonic Analysis on Manifolds 141148
- An application of hypergeometric shift operators to the 𝜒-spherical Fourier transform 143150
- Harmonic analysis of a class of reproducing kernel Hilbert spaces arising from groups 157164
- Approximations in 𝐿_{𝑝}-norms and Besov spaces on compact manifolds 199206
- Back Cover Back Cover1218