A Mathematical Introduction to Wavelets

P. Wojtaszczyk (Professor, Uniwersytet Warszawski, Poland), J. Bruce

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English

Cambridge University Press
14 April 1997

Mathematics & Sciences; Functional analysis & transforms

Series: London Mathematical Society Student Texts

This book presents a mathematical introduction to the theory of orthogonal wavelets and their uses in analyzing 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. The author discusses wavelet decompositions in Lp spaces, Hardy spaces and Besov spaces and provides wavelet characterizations of those spaces. Also included are 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.

By: P. Wojtaszczyk (Professor Uniwersytet Warszawski Poland)
Series edited by: J. Bruce
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 37
Dimensions: Height: 228mm, Width: 151mm, Spine: 18mm
Weight: 380g
ISBN: 9780521578943
ISBN 10: 0521578949
Series: London Mathematical Society Student Texts
Pages: 276
Publication Date: 14 April 1997
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

1. A small sample; 2. General constructions; 3. Some important wavelets; 4. Compactly supported wavelets; 5. Multivariable wavelets; 6. Function spaces; 7. Unconditional convergence; 8. Wavelet bases in Lp and H1; 9. Wavelets and smoothness of functions.

Reviews for A Mathematical Introduction to Wavelets

"""...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"