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Operator methods in wavelets, tilings, and frames / [edited by] Veronika Furst, Keri A. Kornelson and Eric S. Weber.

By: Contributor(s): Material type: TextTextSeries: Contemporary mathematics ; 626.Publication details: Providence : American Mathematical Society, c2014.Description: x, 177 p. : illustrations ; 26 cmISBN:
  • 9781470410407 (pbk : alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512c
Contents:
Phase retrieval by vectors and projections by P. G. Casazza and L. M. Woodland Scalable frames and convex geometry by G. Kutyniok, K. A. Okoudjou, and F. Philipp Dilations of frames, operator-valued measures and bounded linear maps by D. Han, D. R. Larson, B. Liu, and R. Liu Images of the continuous wavelet transform by M. Ghandehari and K. F. Taylor Decompositions of generalized wavelet representations by B. Currey, A. Mayeli, and V. Oussa Exponential splines of complex order by P. Massopust Local translations associated to spectral sets by D. E. Dutkay and J. Haussermann Additive spectra of the 1/4 Cantor measure by P. E. T. Jorgensen, K. A. Kornelson, and K. L. Shuman Necessary density conditions for sampling and interpolation in de Branges spaces by S. al-Sa'di and E. Weber Dynamical sampling in hybrid shift invariant spaces by R. Aceska and S. Tang Dynamical sampling in infinite dimensions with and without a forcing term by J. Davis.
Summary: 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, USA. 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.
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Includes bibliographical references.

Phase retrieval by vectors and projections by P. G. Casazza and L. M. Woodland
Scalable frames and convex geometry by G. Kutyniok, K. A. Okoudjou, and F. Philipp
Dilations of frames, operator-valued measures and bounded linear maps by D. Han, D. R. Larson, B. Liu, and R. Liu
Images of the continuous wavelet transform by M. Ghandehari and K. F. Taylor
Decompositions of generalized wavelet representations by B. Currey, A. Mayeli, and V. Oussa
Exponential splines of complex order by P. Massopust
Local translations associated to spectral sets by D. E. Dutkay and J. Haussermann
Additive spectra of the 1/4 Cantor measure by P. E. T. Jorgensen, K. A. Kornelson, and K. L. Shuman
Necessary density conditions for sampling and interpolation in de Branges spaces by S. al-Sa'di and E. Weber
Dynamical sampling in hybrid shift invariant spaces by R. Aceska and S. Tang
Dynamical sampling in infinite dimensions with and without a forcing term by J. Davis.

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, USA. 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.

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