图书信息
图书目录
调和分析：分析综合教程（第3部分）（影印版）
暂无简介
作者：
Barry Simon
定价：
269.00 元
出版时间：
2023-03-23
ISBN：
978-7-04-059311-2
物料号：
59311-00
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：
1300.000千字
开本：
特殊
装帧形式：
精装
版次：
1
最新版次印刷时间：
2023年
- 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
- 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
