调和分析概览（影印版）

样章

作者：

Steven G. Krantz

定价：

169.00 元

版面字数：

610千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2022年

ISBN：

978-7-04-057027-4

物料号：

57027-00

出版时间：

2022-02-28

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

分析

暂无

目录
- 前辅文
- 0 Overview of Measure Theory and Functional Analysis
  - 0.1 Pre-Basics
  - 0.2 A Whirlwind Review of Measure Theory
  - 0.3 The Elements of Banach Space Theory
  - 0.4 Hilbert Space
  - 0.5 Two Fundamental Principles of Functional Analysis
- 1 Fourier Series Basics
  - 1.0 The Pre-History of Fourier Analysis
  - 1.1 The Rudiments of Fourier Series
  - 1.2 Summability of Fourier Series
  - 1.3 A Quick Introduction to Summability Methods
  - 1.4 Key Properties of Summability Kernels
  - 1.5 Pointwise Convergence for Fourier Series
  - 1.6 Norm Convergence of Partial Sums and the Hilbert Transform
- 2 The Fourier Transform
  - 2.1 Basic Properties of the Fourier Transform
  - 2.2 Invariance and Symmetry Properties of the Fourier Transform
  - 2.3 Convolution and Fourier Inversion
  - 2.4 The Uncertainty Principle
- 3 Multiple Fourier Series
  - 3.1 Various Methods of Partial Summation
  - 3.2 Examples of Different Types of Summation
  - 3.3 Fourier Multipliers and the Summation of Series
  - 3.4 Applications of the Fourier Multiplier Theorems to Summation of Multiple Trigonometric Series
  - 3.5 The Multiplier Problem for the Ball
- 4 Spherical Harmonics
  - 4.1 A New Look at Fourier Analysis in the Plane
  - 4.2 Further Results on Spherical Harmonics
- 5 Fractional Integrals, Singular Integrals, and Hardy Spaces
  - 5.1 Fractional Integrals and Other Elementary Operators
  - 5.2 Prolegomena to Singular Integral Theory
  - 5.3 An Aside on Integral Operators
  - 5.4 A Look at Hardy Spaces in the Complex Plane
  - 5.5 The Real-Variable Theory of Hardy Spaces
  - 5.6 The Maximal-Function Characterization of Hardy Spaces
  - 5.7 The Atomic Theory of Hardy Spaces
  - 5.8 Ode to BMO
- 6 Modern Theories of Integral Operators
  - 6.1 Spaces of Homogeneous Type
  - 6.2 Integral Operators on a Space of Homogeneous Type
  - 6.3 A New Look at Hardy Spaces
  - 6.4 The T .1/ Theorem
- 7 Wavelets
  - 7.1 Localization in the Time and Space Variables
  - 7.2 Building a Custom Fourier Analysis
  - 7.3 The Haar Basis
  - 7.4 Some Illustrative Examples
  - 7.5 Construction of a Wavelet Basis
- 8 A Retrospective
  - 8.1 Fourier Analysis: An Historical Overview
- Appendices and Ancillary Material
  - Appendix I, The Existence of Testing Functions and Their Density in L p
  - Appendix II, Schwartz Functions and the Fourier Transform
  - Appendix III, The Interpolation Theorems of Marcinkiewicz and Riesz-Thorin
  - Appendix IV, Hausdorff Measure and Surface Measure
  - Appendix V, Green’s Theorem
  - Appendix VI, The Banach-Alaoglu Theorem
  - Appendix VII, Expressing an Integral in Terms of the Distribution Function
  - Appendix VIII, The Stone-Weierstrass Theorem
  - Appendix IX, Landau’s O and o Notation
- Table of Notation
- Bibliography
- Index