Littlewood-Paley Theory and the Study of Function Spaces (Cbms Regional Conference Series in Mathema pdf epub mobi txt 电子书下载 2025

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出版者:Amer Mathematical Society

作者:Michael Frazier

出品人:

页数:132

译者:

出版时间:1991-05

价格:USD 46.00

装帧:Paperback

isbn号码:9780821807316

丛书系列:CBMS Regional Conference Series in Mathematics

图书标签:

scnu
数学分析
调和分析
函数空间
Littlewood-Paley理论
傅里叶分析
Cbms
区域会议论文集
实分析
泛函分析
微积分

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具体描述

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 φ-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 φ-transform, wavelet, and smooth atomic expansions are presented as natural extensions of the classical theory. Finally, applications to harmonic analysis (Calderón-Zygmund operators), signal processing (compression), and mathematical physics (potential theory) are discussed.

作者简介

Michael Frazier, Björn Jawerth: University of South Carolina, Columbia, SC,

Guido Weiss: Washington University, St. Louis, MO

目录信息

Cover 1
Title 4
Copyright 5
Contents 6
Preface 8
Introduction 10
1. Caldeórn's Formula and a Decomposition of L[sup(2)(R[sup(n)]) 16Free
2. Decomposition of Lipschitz Spaces28
3. Minimality of B[sup(0, 1)][sub(1)]34
4. Littlewood-Paley Theory42
5. The Besov and Triebel-Lizorkin Spaces50
6. The φ-Transform60
7. Wavelets70
8. Calderón-Zygmund Operators84
9. Potential Theory and a Result of Muckenhoupt-Wheeden100
10. Further Applications108
Appendix122
Bibliography138
Back Cover142
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