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Frames and Operator Theory in Analysis and Signal Processing
About this Title
David R. Larson, Peter Massopust, Zuhair Nashed, Minh Chuong Nguyen, Manos Papadakis and Ahmed Zayed, Editors
Publication: Contemporary Mathematics
Publication Year 2008: Volume 451
ISBNs: 978-0-8218-4144-0 (print); 978-0-8218-8130-9 (online)
MathSciNet review: 2422280
This volume contains articles based on talks presented at the Special Session Frames and Operator Theory in Analysis and Signal Processing, held in San Antonio, Texas, in January of 2006.
Recently, the field of frames has undergone tremendous advancement. Most of the work in this field is focused on the design and construction of more versatile frames and frames tailored towards specific applications, e.g., finite dimensional uniform frames for cellular communication. In addition, frames are now becoming a hot topic in mathematical research as a part of many engineering applications, e.g., matching pursuits and greedy algorithms for image and signal processing. Topics covered in this book include:
Application of several branches of analysis (e.g., PDEs; Fourier, wavelet, and harmonic analysis; transform techniques; data representations) to industrial and engineering problems, specifically image and signal processing.
Theoretical and applied aspects of frames and wavelets.
Pure aspects of operator theory emphasizing the connections to applied mathematics, frames, and signal processing.
This volume will be equally attractive to pure mathematicians working on the foundations of frame and operator theory and their interconnections as it will to applied mathematicians investigating applications and to physicists and engineers employing these designs. It thus may appeal to a wide target group of researchers and may serve as a catalyst for cross-fertilization of several important areas of mathematics and the applied sciences.
Graduate students and research mathematicians interested in pure and applied harmonic analysis, and operator theory.
Table of Contents
- Nikolaos D. Atreas and C. Karanikas – Haar-type orthonormal systems, data presentation as Riesz products and a recognition on symbolic sequences [MR 2422238]
- Peter G. Casazza and Nicole Leonhard – Classes of finite equal norm Parseval frames [MR 2422239]
- Nguyen Minh Chuong and Nguyen Van Co – $p$-adic pseudodifferential operators and wavelets [MR 2422240]
- Elena Cordero and Luigi Rodino – Short-time Fourier transform analysis of localization operators [MR 2422241]
- Jonas D’Andrea, Kathy D. Merrill and Judith Packer – Fractal wavelets of Dutkay-Jorgensen type for the Sierpinski gasket space [MR 2422242]
- Lucia Dettori and Ahmed I. Zayed – Texture identification of tissues using directional wavelet, ridgelet and curvelet transforms [MR 2422243]
- Mihaela Dobrescu and Gestur Ólafsson – Coxeter groups, wavelets, multiresolution and sampling [MR 2422244]
- Christopher Heil and David Larson – Operator theory and modulation spaces [MR 2422245]
- Palle E. T. Jorgensen – Frame analysis and approximation in reproducing kernel Hilbert spaces [MR 2422246]
- Victor Kaftal, David Larson and Shuang Zhang – Operator-valued frames on $C^*$-modules [MR 2422247]
- David R. Larson and Peter Massopust – Coxeter groups and wavelet sets [MR 2422248]
- Christiane Pöschl and Otmar Scherzer – Characterization of minimizers of convex regularization functionals [MR 2422249]
- Gilbert G. Walter and Tatiana Soleski – Error estimates for the PSWF method in MRI [MR 2422250]
- H. Šikić, D. Speegle and G. Weiss – Structure of the set of dyadic PFW’s [MR 2422251]