图书信息
图书目录
实分析：分析综合教程（第1部分）（影印版）
暂无简介
作者：
Barry Simon
定价：
269.00元
出版时间：
2023-03-24
ISBN：
978-7-04-059306-8
物料号：
59306-00
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：
1350.000千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
- 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
- 4.7. Comparison of Measures
- 4.8. Duality for Banach Lattices
- 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
