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  1. Home
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  3. A Mathematical Introduction to Wavelets
  • Cited by 287
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
1997
Online ISBN:
9780511623790
DOI:
https://doi.org/10.1017/CBO9780511623790
Subjects:
Mathematics (general), Mathematics, Abstract Analysis
Series:
London Mathematical Society Student Texts (37)
Information

Book description

This book presents a mathematical introduction to the theory of orthogonal wavelets and their uses in analysing functions and function spaces, both in one and in several variables. Starting with a detailed and self contained discussion of the general construction of one dimensional wavelets from multiresolution analysis, the book presents in detail the most important wavelets: spline wavelets, Meyer's wavelets and wavelets with compact support. It then moves to the corresponding multivariable theory and gives genuine multivariable examples. Wavelet decompositions in Lp spaces, Hardy spaces and Besov spaces are discussed and wavelet characterisations of those spaces are provided. Also included are some additional topics like periodic wavelets or wavelets not associated with a multiresolution analysis. This will be an invaluable book for those wishing to learn about the mathematical foundations of wavelets.

Reviews

"...the book does cover the basic material in a well-organized manner and with detailed explanations about the construction of wavelets. A nice feature of the book is that it has more than a hundred exercises of various levels of difficulty...This monograph is a suitable textbook for an introductory course in modern Fourier analysis and wavelet theory." Rodolfo Torres, Mathematical Reviews, 98j

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