A Mathematical Introduction to Wavelets

The only introduction to wavelets that doesn't avoid the tough mathematical questions.

P. Wojtaszczyk (Author)

9780521570206, Cambridge University Press

Hardback, published 13 February 1997

276 pages, 6 b/w illus.
23.6 x 15.7 x 2 cm, 0.515 kg

"...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

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.

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.

Subject Areas: Functional analysis & transforms [PBKF]