Synopses & Reviews
Over the last two years, wavelet methods have shown themselves to be of considerable use to harmonic analysts and, in particular, advances have been made concerning their applications. The strength of wavelet methods lies in their ability to describe local phenomena more accurately than a traditional expansion in sines and cosines can. Thus, wavelets are ideal in many fields where an approach to transient behaviour is needed, for example, in considering acoustic or seismic signals, or in image processing. Yves Meyer stands the theory of wavelets firmly upon solid ground by basing his book on the fundamental work of Calderón, Zygmund and their collaborators. For anyone who would like an introduction to wavelets, this book will prove to be a necessary purchase.
Review
'I recommend this book to every mathematically minded reader ... it is beautifully written and the English translation is excellent.' Science
Review
'... an excellent introduction to wavelets by a leading researcher in this field. This lucid account of the theory behind wavelets is aimed at the postgraduate level.' Short Book Reviews
Synopsis
The definite mathematical treatment of this important area, written by one of the founders of the field.
Synopsis
Yves Meyer stands the theory of wavelets firmly upon solid ground by basing his book on the fundamental work of Calderón, Zygmund and their collaborators. For anyone who would like an introduction to wavelets, this book will prove to be a necessary purchase.
Synopsis
In recent years the mathematical theory of wavelets has shown itself to be a tool of considerable power to harmonic analysts, and one that provides an alternative to the standard theory of Fourier analysis. The strength of wavelets lies in their ability to describe local phenomena more accurately than a traditional expansion in sines and cosines can. Thus, wavelets are ideal in any fields where an approach to transient behavior is needed, for example, in considering acoustic or seismic signals, or image processing. This is the first real textbook on wavelets. The aim of the book is to describe the foundations of the so-called wavelet analysis, emphasizing its roots in mathematics, particularly the pioneering work of Calderón and Zygmund.
Table of Contents
Introduction; 1. Fourier series and integrals, filtering and sampling; 2. Multiresolution approximation of L2(Rn); 3. Orthonormal wavelet bases; 4. Non-orthogonal wavelets; 5. Wavelets, the Hardy space H1, and its dual BMO; 6. Wavelets and spaces of functions and distributions; References.