实分析：分析综合教程（第1部分）（影印版）

样章

作者：

Barry Simon

定价：

269.00 元

版面字数：

1350千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2023年

ISBN：

978-7-04-059306-8

物料号：

59306-00

出版时间：

2023-03-24

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. Metric Spaces
  - 1.3. The Real Numbers
  - 1.4. Orders
  - 1.5. The Axiom of Choice and Zorn’s Lemma
  - 1.6. Countability
  - 1.7. Some Linear Algebra
  - 1.8. Some Calculus
- Chapter 2. Topological Spaces
  - 2.1. Lots of Definitions
  - 2.2. Countability and Separation Properties
  - 2.3. Compact Spaces
  - 2.4. The Weierstrass Approximation Theorem and Bernstein Polynomials
  - 2.5. The Stone–Weierstrass Theorem
  - 2.6. Nets
  - 2.7. Product Topologies and Tychonoff’s Theorem
  - 2.8. Quotient Topologies
- Chapter 3. A First Look at Hilbert Spaces and Fourier Series
  - 3.1. Basic Inequalities
  - 3.2. Convex Sets, Minima, and Orthogonal Complements
  - 3.3. Dual Spaces and the Riesz Representation Theorem
  - 3.4. Orthonormal Bases, Abstract Fourier Expansions, and Gram–Schmidt
  - 3.5. Classical Fourier Series
  - 3.6. The Weak Topology
  - 3.7. A First Look at Operators
  - 3.8. Direct Sums and Tensor Products of Hilbert Spaces
- Chapter 4. Measure Theory
  - 4.1. Riemann–Stieltjes Integrals
  - 4.2. The Cantor Set, Function, and Measure
  - 4.3. Bad Sets and Good Sets
  - 4.4. Positive Functionals and Measures via L1(X)
  - 4.5. The Riesz–Markov Theorem
  - 4.6. Convergence Theorems; Lp Spaces
  - 4.7. Comparison of Measures
  - 4.8. Duality for Banach Lattices; Hahn and Jordan Decomposition
  - 4.9. Duality for Lp
  - 4.10. Measures on Locally Compact and σ-Compact Spaces
  - 4.11. Product Measures and Fubini’s Theorem
  - 4.12. Infinite Product Measures and Gaussian Processes
  - 4.13. General Measure Theory
  - 4.14. Measures on Polish Spaces
  - 4.15. Another Look at Functions of Bounded Variation
  - 4.16. Bonus Section: Brownian Motion
  - 4.17. Bonus Section: The Hausdorff Moment Problem
  - 4.18. Bonus Section: Integration of Banach Space-Valued Functions
  - 4.19. Bonus Section: Haar Measure on σ-Compact Groups
- Chapter 5. Convexity and Banach Spaces
  - 5.1. Some Preliminaries
  - 5.2. H¨older’s and Minkowski’s Inequalities: A Lightning Look
  - 5.3. Convex Functions and Inequalities
  - 5.4. The Baire Category Theorem and Applications
  - 5.5. The Hahn–Banach Theorem
  - 5.6. Bonus Section: The Hamburger Moment Problem
  - 5.7. Weak Topologies and Locally Convex Spaces
  - 5.8. The Banach–Alaoglu Theorem
  - 5.9. Bonus Section: Minimizers in Potential Theory
  - 5.10. Separating Hyperplane Theorems
  - 5.11. The Krein–Milman Theorem
  - 5.12. Bonus Section: Fixed Point Theorems and Applications
- Chapter 6. Tempered Distributions and the Fourier Transform
  - 6.1. Countably Normed and Fr´echet Spaces
  - 6.2. Schwartz Space and Tempered Distributions
  - 6.3. Periodic Distributions
  - 6.4. Hermite Expansions
  - 6.5. The Fourier Transform and Its Basic Properties
  - 6.6. More Properties of Fourier Transform
  - 6.7. Bonus Section: Riesz Products
  - 6.8. Fourier Transforms of Powers and Uniqueness of Minimizers in Potential Theory
  - 6.9. Constant Coefficient Partial Differential Equations
- Chapter 7. Bonus Chapter: Probability Basics
  - 7.1. The Language of Probability
  - 7.2. Borel–Cantelli Lemmas and the Laws of Large Numbers and of the Iterated Logarithm
  - 7.3. Characteristic Functions and the Central Limit Theorem
  - 7.4. Poisson Limits and Processes
  - 7.5. Markov Chains
- Chapter 8. Bonus Chapter: Hausdorff Measure and Dimension
  - 8.1. The Carath´eodory Construction
  - 8.2. Hausdorff Measure and Dimension
- Chapter 9. Bonus Chapter: Inductive Limits and Ordinary Distributions
  - 9.1. Strict Inductive Limits
  - 9.2. Ordinary Distributions and Other Examples of Strict Inductive Limits
- Bibliography
- Symbol Index
- Subject Index
- Author Index
- Index of Capsule Biographies