Littlewood-Paley Theory and the Study of Function Spaces (Cbms Regional Conference Series in Mathematics) - Softcover

Michael Frazier, Bjorn Jawerth, And Guido Weiss

Softcover

ISBN 10: 0821807315 ISBN 13: 9780821807316

Publisher: American Mathematical Society, 1991

Synopsis

Littlewood-Paley theory was developed to study function spaces in harmonic analysis and partial differential equations. Recently, it has contributed to the development of the $\varphi$-transform and wavelet decompositions. Based on lectures presented at the NSF-CBMS Regional Research Conference on Harmonic Analysis and Function Spaces, held at Auburn University in July 1989, this book is aimed at mathematicians, as well as mathematically literate scientists and engineers interested in harmonic analysis or wavelets. The authors provide not only a general understanding of the area of harmonic analysis relating to Littlewood-Paley theory and atomic and wavelet decompositions, but also some motivation and background helpful in understanding the recent theory of wavelets. The book begins with some simple examples which provide an overview of the classical Littlewood-Paley theory. The $\varphi$-transform, wavelet, and smooth atomic expansions are presented as natural extensions of the classical theory. Finally, applications to harmonic analysis (Calderon-Zygmund operators), signal processing (compression), and mathematical physics (potential theory) are discussed.

About this title

Review

This monograph is an important and welcome addition to the growing literature in this area. -- Mathematical Reviews

Useful for graduate students and researchers with interest in function spaces, approximation theory or wavelet theory. --Zentralblatt für Mathematik

Edition details

• Publisher: American Mathematical Society
• Publication date: 1991
• ISBN 10: 0821807315
• ISBN 13: 9780821807316
• Binding: Paperback
• Language: English
• Number of pages: 132