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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
ISBN：
978-7-04-059316-7
版面字数：
1289.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
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
  • 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

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