调和分析：分析综合教程（第3部分）（影印版）

样章

作者：

Barry Simon

定价：

269.00 元

版面字数：

1300千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2023年

ISBN：

978-7-04-059311-2

物料号：

59311-00

出版时间：

2023-03-23

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
- Chapter 1. Preliminaries
  - 1.1. Notation and Terminology
  - 1.2. Some Results for Real Analysis
  - 1.3. Some Results from Complex Analysis
  - 1.4. Green’s Theorem
- Chapter 2. Pointwise Convergence Almost Everywhere
  - 2.1. The Magic of Maximal Functions
  - 2.2. Distribution Functions, Weak-L1, and Interpolation
  - 2.3. The Hardy–Littlewood Maximal Inequality
  - 2.4. Differentiation and Convolution
  - 2.5. Comparison of Measures
  - 2.6. The Maximal and Birkhoff Ergodic Theorems
  - 2.7. Applications of the Ergodic Theorems
  - 2.8. Bonus Section: More Applications of the Ergodic Theorems
  - 2.9. Bonus Section: Subadditive Ergodic Theorem and Lyapunov Behavior
  - 2.10. Martingale Inequalities and Convergence
  - 2.11. The Christ–Kiselev Maximal Inequality and Pointwise Convergence of Fourier Transforms
- Chapter 3. Harmonic and Subharmonic Functions
  - 3.1. Harmonic Functions
  - 3.2. Subharmonic Functions
  - 3.3. Bonus Section: The Eremenko–Sodin Proof of Picard’s Theorem
  - 3.4. Perron’s Method, Barriers, and Solution of the Dirichlet Problem
  - 3.5. Spherical Harmonics
  - 3.6. Potential Theory
  - 3.7. Bonus Section: Polynomials and Potential Theory
  - 3.8. Harmonic Function Theory of Riemann Surfaces
- Chapter 4. Bonus Chapter: Phase Space Analysis
  - 4.1. The Uncertainty Principle
  - 4.2. The Wavefront Sets and Products of Distributions
  - 4.3. Microlocal Analysis: A First Glimpse
  - 4.4. Coherent States
  - 4.5. Gabor Lattices
  - 4.6. Wavelets
- Chapter 5. Hp Spaces and Boundary Values of Analytic Functions on the Unit Disk
  - 5.1. Basic Properties of Hp
  - 5.2. H2
  - 5.3. First Factorization (Riesz) and Hp
  - 5.4. Caratheodory Functions, h1, and the Herglotz Representation
  - 5.5. Boundary Value Measures
  - 5.6. Second Factorization (Inner and Outer Functions)
  - 5.7. Conjugate Functions and M. Riesz’s Theorem
  - 5.8. Homogeneous Spaces and Convergence of Fourier Series
  - 5.9. Boundary Values of Analytic Functions in the Upper Half-Plane
  - 5.10. Beurling’s Theorem
  - 5.11. Hp-Duality and BMO
  - 5.12. Cotlar’s Theorem on Ergodic Hilbert Transforms
- Chapter 6. Bonus Chapter: More Inequalities
  - 6.1. Lorentz Spaces and Real Interpolation
  - 6.2. Hardy-Littlewood–Sobolev and Stein–Weiss Inequalities
  - 6.3. Sobolev Spaces; Sobolev and Rellich–Kondrachov Embedding Theorems
  - 6.4. The Calderon–Zygmund Method
  - 6.5. Pseudodifferential Operators on Sobolev Spaces and the Calderon–Vaillancourt Theorem
  - 6.6. Hypercontractivity and Logarithmic Sobolev Inequalities
  - 6.7. Lieb–Thirring and Cwikel–Lieb–Rosenblum Inequalities
  - 6.8. Restriction to Submanifolds
  - 6.9. Tauberian Theorems
- Bibliography
- Symbol Index
- Subject Index
- Author Index
- Index of Capsule Biographies