**Contemporary Mathematics**

Volume: 626;
2014;
177 pp;
Softcover

MSC: Primary 41; 42; 43; 46; 47; 94;

Print ISBN: 978-1-4704-1040-7

Product Code: CONM/626

List Price: $66.00

AMS Member Price: $52.80

MAA Member Price: $59.40

**Electronic ISBN: 978-1-4704-1957-8
Product Code: CONM/626.E**

List Price: $66.00

AMS Member Price: $52.80

MAA Member Price: $59.40

# Operator Methods in Wavelets, Tilings, and Frames

Share this page *Edited by *
*Veronika Furst; Keri A. Kornelson; Eric S. Weber*

This volume contains the proceedings of the AMS Special Session on
Harmonic Analysis of Frames, Wavelets, and Tilings, held April
13–14, 2013, in Boulder, Colorado.

Frames were first introduced by Duffin and Schaeffer in 1952 in the
context of nonharmonic Fourier series but have enjoyed widespread
interest in recent years, particularly as a unifying concept. Indeed,
mathematicians with backgrounds as diverse as classical and modern
harmonic analysis, Banach space theory, operator algebras, and complex
analysis have recently worked in frame theory. Frame theory appears
in the context of wavelets, spectra and tilings, sampling theory, and
more.

The papers in this volume touch on a wide variety of topics,
including: convex geometry, direct integral decompositions, Beurling
density, operator-valued measures, and splines. These varied topics
arise naturally in the study of frames in finite and infinite
dimensions. In nearly all of the papers, techniques from operator
theory serve as crucial tools to solving problems in frame theory.

This volume will be of interest not only to researchers in frame
theory but also to those in approximation theory, representation
theory, functional analysis, and harmonic analysis.

#### Readership

Graduate students and research mathematicians interested in linear algebra, functional analysis, and operator theory.

# Table of Contents

## Operator Methods in Wavelets, Tilings, and Frames

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- Participants ix10 free
- Phase retrieval by vectors and projections 112 free
- Scalable frames and convex geometry 1930
- Dilations of frames, operator-valued measures and bounded linear maps 3344
- Images of the continuous wavelet transform 5566
- Decompositions of generalized wavelet representations 6778
- Exponential splines of complex order 8798
- Local translations associated to spectral sets 107118
- Additive spectra of the 1/4 Cantor measure 121132
- Necessary density conditions for sampling and interpolation in de Branges spaces 129140
- Dynamical sampling in hybrid shift invariant spaces 149160
- Dynamical sampling in infinite dimensions with and without a forcing term 167178
- Back Cover Back Cover1192