算子理论: 分析综合教程（第4部分）（影印版）

样章

作者：

Barry Simon

定价：

269.00 元

版面字数：

1289千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2023年

ISBN：

978-7-04-059316-7

物料号：

59316-00

出版时间：

2023-03-15

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 Complex Analysis
  - §1.3. Some Linear Algebra
  - §1.4. Finite-Dimensional Eigenvalue Perturbation Theory
  - §1.5. Some Results from Real Analysis
- Chapter 2. Operator Basics
  - §2.1. Topologies and Special Classes of Operators
  - §2.2. The Spectrum
  - §2.3. The Analytic Functional Calculus
  - §2.4. The Square Root Lemma and the Polar Decomposition
- Chapter 3. Compact Operators, Mainly on a Hilbert Space
  - §3.1. Compact Operator Basics
  - §3.2. The Hilbert–Schmidt Theorem
  - §3.3. The Riesz–Schauder Theorem
  - §3.4. Ringrose Structure Theorems
  - §3.5. Singular Values and the Canonical Decomposition
  - §3.6. The Trace and Trace Class
  - §3.7. Bonus Section: Trace Ideals
  - §3.8. Hilbert–Schmidt Operators
  - §3.9. Schur Bases and the Schur–Lalesco–Weyl Inequality
  - §3.10. Determinants and Fredholm Theory
  - §3.11. Operators with Continuous Integral Kernels
  - §3.12. Lidskii’s Theorem
  - §3.13. Bonus Section: Regularized Determinants
  - §3.14. Bonus Section: Weyl’s Invariance Theorem
  - §3.15. Bonus Section: Fredholm Operators and Their Index
  - §3.16. Bonus Section: M. Riesz’s Criterion
- Chapter 4. Orthogonal Polynomials
  - §4.1. Orthogonal Polynomials on the Real Line and Favard’s Theorem
  - §4.2. The Bochner–Brenke Theorem
  - §4.3. L2- and L∞-Variational Principles: Chebyshev Polynomials
  - §4.4. Orthogonal Polynomials on the Unit Circle: Verblunsky’s and Szeg˝o’s Theorems
- Chapter 5. The Spectral Theorem
  - §5.1. Three Versions of the Spectral Theorem: Resolutions of the Identity, the Functional Calculus, and Spectral Measures
  - §5.2. Cyclic Vectors
  - §5.3. A Proof of the Spectral Theorem
  - §5.4. Bonus Section: Multiplicity Theory
  - §5.5. Bonus Section: The Spectral Theorem for Unitary Operators
  - §5.6. Commuting Self-adjoint and Normal Operators
  - §5.7. Bonus Section: Other Proofs of the Spectral Theorem
  - §5.8. Rank-One Perturbations
  - §5.9. Trace Class and Hilbert–Schmidt Perturbations
- Chapter 6. Banach Algebras
  - §6.1. Banach Algebra: Basics and Examples
  - §6.2. The Gel’fand Spectrum and Gel’fand Transform
  - §6.3. Symmetric Involutions
  - §6.4. Commutative Gel’fand–Naimark Theorem and the Spectral Theorem for Bounded Normal Operators
  - §6.5. Compactifications
  - §6.6. Almost Periodic Functions
  - §6.7. The GNS Construction and the Noncommutative Gel’fand–Naimark Theorem
  - §6.8. Bonus Section: Representations of Locally Compact Groups
  - §6.9. Bonus Section: Fourier Analysis on LCA Groups
  - §6.10. Bonus Section: Introduction to Function Algebras
  - §6.11. Bonus Section: The L1(R) Wiener and Ingham Tauberian Theorems
  - §6.12. The Prime Number Theorem via Tauberian Theorems
- Chapter 7. Bonus Chapter: Unbounded Self-adjoint Operators
  - §7.1. Basic Definitions and the Fundamental Criterion for Self-adjointness
  - §7.2. The Spectral Theorem for Unbounded Operators
  - §7.3. Stone’s Theorem
  - §7.4. von Neumann’s Theory of Self-adjoint Extensions
  - §7.5. Quadratic Form Methods
  - §7.6. Pointwise Positivity and Semigroup Methods
  - §7.7. Self-adjointness and the Moment Problem
  - §7.8. Compact, Rank-One and Trace Class Perturbations
  - §7.9. The Birman–Schwinger Principle
- Bibliography
- Symbol Index
- Subject Index
- Author Index
- Index of Capsule Biographies