Wavelet theory
著者
書誌事項
Wavelet theory
（Translations of mathematical monographs, v. 239）
American Mathematical Society, c2011
- タイトル別名
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Теория всплесков
Teorii︠a︡ vspleskov
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注記
Translation of: Теория всплесков. Москва : Физматлит, 2005
Includes bibliographical references (p. 493-504) and index
内容説明・目次
内容説明
Wavelet theory lies on the crossroad of pure and computational mathematics, with connections to audio and video signal processing, data compression, and information transmission. The present book is devoted to a systematic exposition of modern wavelet theory. It details the construction of orthogonal and biorthogonal systems of wavelets and studies their structural and approximation properties, starting with basic theory and ending with special topics and problems. The book also presents some applications of wavelets. Historical commentary is supplied for each chapter in the book, and most chapters contain exercises. The book is intended for professional mathematicians and graduate students working in functional analysis and approximation theory. It is also useful for engineers applying wavelet theory in their work. Prerequisites for reading the book consist of graduate courses in real and functional analysis.
目次
Preface
Wavelets on the line
Multivariate wavelets
Compactly supported refinable functions
Wavelets with compact support
Fractal properties of wavelets
Factorization of refinement equations
Smoothness of compactly supported wavelets
Nonstationary wavelets
Periodic wavelets
Approximation by periodic wavelets
Remarkable properties of wavelet bases
Auxiliary facts of the theory of functions and functional analysis
Historical comments
Bibliography
Index
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