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Softcover ISBN:  9781470410407 
Product Code:  CONM/626 
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Softcover ISBN:  9781470410407 
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Book DetailsContemporary MathematicsVolume: 626; 2014; 177 ppMSC: Primary 41; 42; 43; 46; 47; 94
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, operatorvalued 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.
ReadershipGraduate students and research mathematicians interested in linear algebra, functional analysis, and operator theory.

Table of Contents

Articles

Peter G. Casazza and Lindsey M. Woodland — Phase retrieval by vectors and projections

Gitta Kutyniok, Kasso A. Okoudjou and Friedrich Philipp — Scalable frames and convex geometry

Deguang Han, David R. Larson, Bei Liu and Rui Liu — Dilations of frames, operatorvalued measures and bounded linear maps

Mahya Ghandehari and Keith F. Taylor — Images of the continuous wavelet transform

Bradley Currey, Azita Mayeli and Vignon Oussa — Decompositions of generalized wavelet representations

Peter Massopust — Exponential splines of complex order

Dorin Ervin Dutkay and John Haussermann — Local translations associated to spectral sets

Palle E. T. Jorgensen, Keri A. Kornelson and Karen L. Shuman — Additive spectra of the $\frac 14$ Cantor measure

Sa’ud alSa’di and Eric Weber — Necessary density conditions for sampling and interpolation in de Branges spaces

Roza Aceska and Sui Tang — Dynamical sampling in hybrid shift invariant spaces

Jacqueline Davis — Dynamical sampling in infinite dimensions with and without a forcing term


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

Articles

Peter G. Casazza and Lindsey M. Woodland — Phase retrieval by vectors and projections

Gitta Kutyniok, Kasso A. Okoudjou and Friedrich Philipp — Scalable frames and convex geometry

Deguang Han, David R. Larson, Bei Liu and Rui Liu — Dilations of frames, operatorvalued measures and bounded linear maps

Mahya Ghandehari and Keith F. Taylor — Images of the continuous wavelet transform

Bradley Currey, Azita Mayeli and Vignon Oussa — Decompositions of generalized wavelet representations

Peter Massopust — Exponential splines of complex order

Dorin Ervin Dutkay and John Haussermann — Local translations associated to spectral sets

Palle E. T. Jorgensen, Keri A. Kornelson and Karen L. Shuman — Additive spectra of the $\frac 14$ Cantor measure

Sa’ud alSa’di and Eric Weber — Necessary density conditions for sampling and interpolation in de Branges spaces

Roza Aceska and Sui Tang — Dynamical sampling in hybrid shift invariant spaces

Jacqueline Davis — Dynamical sampling in infinite dimensions with and without a forcing term