（已有2条评价）基本信息
- 原书名：Classical Fourier Analysis, Second Edition
- 原出版社： Springer
- 作者： (美)Loukas Grafakos
- 丛书名： Graduate Texts in Mathematics
- 出版社：世界图书出版公司
- ISBN：9787510040610
- 上架时间：2013-10-28
- 出版日期：2012 年1月
- 开本：24开
- 页码：489
- 版次：2-1
- 所属分类：数学 > 分析 > 傅里叶分析与小波分析
编辑推荐
第二版为两卷集，旨在为读者提供学习欧几里得调和解析领域的理论基础。
内容简介
目录
《经典傅里叶分析(第2版)(英文版)》
LP Spaces and Interpolation
1.1 Lp and Weak LP
1.2 Convolution and Approximate Identifies
1.3 Interpolation
1.4 Lorentz Spaces
2 Maximal Functions, Fourier Transform, and Distributions
2.1 Maximal Functions
2.2 The Schwartz Class and the Fourier Transform
2.3 The Class of Tempered Distributions
2.4 More About Distributions and the Fourier Transform
2.5 Convolution Operators on Lp Spaces and Multipliers
2.6 Oscillatory Integrals
3 Fourier Analysis on the Torus
3.1 Fourier Coefficients
3.2 Decay of Fourier Coefficients
3.3 Pointwise Convergence of Fourier Series
3.4 Divergence of Fourier and Bochner-Riesz Summability
3.5 The Conjugate Function and Convergence in Norm
3.6 Multipliers, Transference, and Almost Everywhere Convergence
LP Spaces and Interpolation
1.1 Lp and Weak LP
1.2 Convolution and Approximate Identifies
1.3 Interpolation
1.4 Lorentz Spaces
2 Maximal Functions, Fourier Transform, and Distributions
2.1 Maximal Functions
2.2 The Schwartz Class and the Fourier Transform
2.3 The Class of Tempered Distributions
2.4 More About Distributions and the Fourier Transform
2.5 Convolution Operators on Lp Spaces and Multipliers
2.6 Oscillatory Integrals
3 Fourier Analysis on the Torus
3.1 Fourier Coefficients
3.2 Decay of Fourier Coefficients
3.3 Pointwise Convergence of Fourier Series
3.4 Divergence of Fourier and Bochner-Riesz Summability
3.5 The Conjugate Function and Convergence in Norm
3.6 Multipliers, Transference, and Almost Everywhere Convergence
前言
The great response to the publication of the book Classical and Modern Fourier Analysis has been very gratifying. I amdelighted that Springer has offered to publish the second edition of this book in two volumes: Classical Fourier Analysis, 2nd Edition, and Modern Fourier Analysis, 2nd Edition.
These volumes are mainly addressed to graduate students who wish to study Fourier analysis. This first volume is intended to serve as a text for a one-semester course in the subject. The prerequisite for understanding the material herein is satisfactory completion of courses in measure theory, Lebesgue integration, and complex variables.
The details included in the proofs make the exposition longer. Although it willbehoove many readers to skim through the more technical aspects of the presentation and concentrate on the flow of ideas, the fact that details are present will be comforting to some. The exercises at the end of each section enrich the material of the corresponding section and provide an opportunity to develop additional intuition and deeper comprehension. The historical notes of each chapter are intended to provide an account of past research but also to suggest directions for further investigation. The appendix includes miscellaneous auxiliary material needed throughout the text.
A web site for the book is maintained at
http://math.missouri.edu/,,,loukas/FourierAnalysis.html I am solely responsible for any misprints, mistakes, and historical omissions in this book. Please contact me directly (loukas@math.missouri.edu) if you have corrections, comments, suggestions for improvements, or questions.
Columbia, Missouri, Loukas Grafakos
April 2008
These volumes are mainly addressed to graduate students who wish to study Fourier analysis. This first volume is intended to serve as a text for a one-semester course in the subject. The prerequisite for understanding the material herein is satisfactory completion of courses in measure theory, Lebesgue integration, and complex variables.
The details included in the proofs make the exposition longer. Although it willbehoove many readers to skim through the more technical aspects of the presentation and concentrate on the flow of ideas, the fact that details are present will be comforting to some. The exercises at the end of each section enrich the material of the corresponding section and provide an opportunity to develop additional intuition and deeper comprehension. The historical notes of each chapter are intended to provide an account of past research but also to suggest directions for further investigation. The appendix includes miscellaneous auxiliary material needed throughout the text.
A web site for the book is maintained at
http://math.missouri.edu/,,,loukas/FourierAnalysis.html I am solely responsible for any misprints, mistakes, and historical omissions in this book. Please contact me directly (loukas@math.missouri.edu) if you have corrections, comments, suggestions for improvements, or questions.
Columbia, Missouri, Loukas Grafakos
April 2008
