图书信息
图书目录
算子理论: 分析综合教程（第4部分）（影印版）
暂无简介
作者：
Barry Simon
定价：
269.00元
出版时间：
2023-03-15
ISBN：
978-7-04-059316-7
物料号：
59316-00
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：
1289.000千字
开本：
16开
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. 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
