图书信息
图书目录
调和分析概览（影印版）
暂无简介
作者：
Steven G. Krantz
定价：
169.00元
出版时间：
2022-02-28
ISBN：
978-7-04-057027-4
物料号：
57027-00
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
重点项目：
暂无
版面字数：
610.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
- 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
