Wavelet Theory ( Translations of Mathematical Monographs )

Publication series : Translations of Mathematical Monographs

Author: I. Ya. Novikov;V. Yu. Protasov;M. A. Skopina  

Publisher: American Mathematical Society‎

Publication year: 2011

E-ISBN: 9781470416256

P-ISBN(Paperback): 9780821849842

Subject: O174.2 classical harmonic analysis (Fourier analysis)

Keyword: 数学

Language: ENG

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Wavelet Theory

Description

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.

Chapter

Title page

Contents

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

Back Cover

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