Operator Methods in Wavelets, Tilings, and Frames

Operator Methods in Wavelets, Tilings, and Frames

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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, 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.What can we say about the dilation of I†? Does it admit a Hilbert space dilation? Yes. An affirmative answer would yield a negative answer to the similarity problem. Problem 6. Let A aŠ‚ B(K) be a von Neumann algebra, and let I† : A a†’ B( H) be aanbsp;...

Title:Operator Methods in Wavelets, Tilings, and Frames
Author:Keri A. Kornelson, Eric S. Weber
Publisher:American Mathematical Soc. - 2014-10-20


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