The Functional And Harmonic Analysis Of Wavelets And Frames
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The Functional And Harmonic Analysis Of Wavelets And Frames
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Author : Lawrence W. Baggett
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
The Functional And Harmonic Analysis Of Wavelets And Frames written by Lawrence W. Baggett and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Over the past decade, wavelets and frames have emerged as increasingly powerful tools of analysis on $n$-dimension Euclidean space. Both wavelets and frames were studied initially by using classical Fourier analysis. However, in recent years more abstract tools have been introduced, for example, from operator theory, abstract harmonic analysis, von Neumann algebras, etc. The editors of this volume organized a Special Session on the functional and harmonic analysis of wavelets at the San Antonio (TX) Joint Mathematics Meetings. The goal of the session was to focus research attention on these newly-introduced tools and to share the organizers' view that this modern application holds the promise of providing some deeper understanding and fascinating new structures in pure functional analysis. This volume presents the fruitful results of the lively discussions that took place at the conference
An Introduction To Frames And Riesz Bases
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Author : Ole Christensen
language : en
Publisher: Birkhäuser
Release Date : 2016-05-24
An Introduction To Frames And Riesz Bases written by Ole Christensen and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-24 with Mathematics categories.
This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field. Key features include: *Elementary introduction to frame theory in finite-dimensional spaces * Basic results presented in an accessible way for both pure and applied mathematicians * Extensive exercises make the work suitable as a textbook for use in graduate courses * Full proofs includ ed in introductory chapters; only basic knowledge of functional analysis required * Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems * Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory * Selected research topics presented with recommendations for more advanced topics and further readin g * Open problems to stimulate further research An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference. Review of the first edition: "Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field ... . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research." — Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005
Gabor And Wavelet Frames
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Author : Zuowei Shen
language : en
Publisher: World Scientific
Release Date : 2007-08-13
Gabor And Wavelet Frames written by Zuowei Shen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-13 with Mathematics categories.
Gabor and wavelet analyses have found widespread applications in signal analysis, image processing and many other information-related areas. Both deliver representations that are simultaneously local in time and in frequency. Due to their significance and success in practical applications, they formed some of the core topics of the program “Mathematics and Computation in Imaging Science and Information Processing”, which was held at the Institute for Mathematical Sciences, National University of Singapore, from July to December 2003 and in August 2004. As part of the program, tutorial lectures were conducted by international experts, and they covered a wide spectrum of topics in mathematical image, signal and information processing.This volume includes exposition articles by the tutorial speakers on the foundations of Gabor analysis, subband filters and wavelet algorithms, and operator-theoretic interpolation of wavelets and frames. It also presents research papers on Gabor analysis, written by specialists in their respective areas. The volume takes graduate students and researchers new to the field on a valuable learning journey from introductory Gabor and wavelet analyses to advanced topics of current research.
Wavelets Frames And Operator Theory
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Author : Palle E. T. Jørgensen
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Wavelets Frames And Operator Theory written by Palle E. T. Jørgensen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Nineteen papers are presented from a special joint session held in conjunction with the American Mathematical Society's 2003 annual meeting in Baltimore, and a National Science Foundation workshop at the University of Maryland. The papers distinguish themselves by often including applications as wel
Representations Wavelets And Frames
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Author : Palle E. T. Jorgensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-29
Representations Wavelets And Frames written by Palle E. T. Jorgensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-29 with Mathematics categories.
The work of Lawrence Baggett has had a profound impact on the field of abstract harmonic analysis and the many areas of mathematics that use its techniques. His sphere of influence ranges from purely theoretical results regarding the representations of locally compact groups to recent applications of wavelets and frames to problems in sampling theory and image compression. Contributions in this volume reflect this broad scope, and Baggett’s unusual ability to bring together techniques from disparate fields. Recent applications to problems in sampling theory and image compression are included.
Frames And Operator Theory In Analysis And Signal Processing
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Author : David R. Larson
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Frames And Operator Theory In Analysis And Signal Processing written by David R. Larson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Harmonic Analysis And Applications
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Author : Christopher Heil
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-02
Harmonic Analysis And Applications written by Christopher Heil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-02 with Mathematics categories.
This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto’s achievements and expresses an appreciation for the mathematical and personal inspiration he has given to so many students, co-authors, and colleagues.
Wavelet Analysis And Applications
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Author : Tao Qian
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-24
Wavelet Analysis And Applications written by Tao Qian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-24 with Mathematics categories.
This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics. Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationary Signals Applications, particularly in image processing Through the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.
Foundations Of Time Frequency Analysis
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Author : Karlheinz Gröchenig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Foundations Of Time Frequency Analysis written by Karlheinz Gröchenig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Technology & Engineering categories.
Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.
Wavelets And Multiscale Analysis
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Author : Jonathan Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-01
Wavelets And Multiscale Analysis written by Jonathan Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Mathematics categories.
Since its emergence as an important research area in the early 1980s, the topic of wavelets has undergone tremendous development on both theoretical and applied fronts. Myriad research and survey papers and monographs have been published on the subject, documenting different areas of applications such as sound and image processing, denoising, data compression, tomography, and medical imaging. The study of wavelets remains a very active field of research, and many of its central techniques and ideas have evolved into new and promising research areas. This volume, a collection of invited contributions developed from talks at an international conference on wavelets, is divided into three parts: Part I is devoted to the mathematical theory of wavelets and features several papers on wavelet sets and the construction of wavelet bases in different settings. Part II looks at the use of multiscale harmonic analysis for understanding the geometry of large data sets and extracting information from them. Part III focuses on applications of wavelet theory to the study of several real-world problems. Overall, the book is an excellent reference for graduate students, researchers, and practitioners in theoretical and applied mathematics, or in engineering.