内勒、塞尔编写的《工程与科学中的线性算子理论(英文版)》旨在为工程师、科研工作者和应用数学工作者提供适用于他们的泛函分析的基础知识。尽管书中采取的是定义-定理-证明的数学模式，但是该书在所涵盖知识点的选取和解释说明方面还是下了很大的功夫。该书也可以被用作高级教程，为了便于不同知识背景的学生学习，书中附录部分涵盖了许多有益的数学课题。

Preface

 Chapter 1 Introduction

  1. Black Boxes

  2. Structure of the Plane

  3. Mathematical Modeling

  4. The Axiomatic Method. The

  Process of Abstraction

  5. Proofs of Theorems

 Chapter 2 Set-Theoretic Structure

  1. Introduction

  2. Basic Set Operations

  3. Cartesian Products

  4. Sets of Numbers

  5. Equivalence Relations and

  Partitions

  6. Functions

  7. Inverses

  8. Systems Types

 Chapter 3 Topological Structure

  1. Introduction

  Port A Introduction to Metric Spaces

  2. Metric Spaces: Definition

  3. Examples of Metric Spaces

  4. Subspaces and Product Spaces

  5. Continuous Functions

  6. Convergent Sequences

  7. A Connection Between

  Continuity and Convergence

  Part B Some Deeper Metric

  Space Concepts

  8. Local Neighborhoods

  9. Open Sets

  10. More on Open Sets

  11. Examples of Homeomorphic

  Metric Spaces

  12. Closed Sets and the Closure

  Operation

  13. Completeness

  14. Completion of Metric Spaces

  15. Contraction Mapping

  16. Total Boundexlness and

  Approximations

  17. Compactness

 Chapter 4 Algebraic Structure

  1. Introduction

  Part A Introduction to Linear Spaces

  2. Linear Spaces and Linear

  Subspaces

  3. Linear Transformations

  4. Inverse Transformations

  5. Isomorphisms

  6. Linear Independence and

  Dependence

  7. Hamel Bases and Dimension

  8. The Use of Matrices to Represent

  Linear Transformations

  9. Equivalent Linear

  Transformations

  Part B Further Topics

  10. Direct Sums and Sums

  11. Projections

  12. Linear Functionals and the Alge-

  braic Conjugate of a Linear Space

  13. Transpose of a Linear

  Transformation

 Chapter 5 Combined Topological

  and Algebraic Structure

  1. Introduction

  Part A Banach Spaces

  2. Definitions

  3. Examples of Normal Linear

  Spaces

  4. Sequences and Series

  5. Linear Subspaces

  6. Continuous Linear

  Transformations

  7. Inverses and Continuous Inverses

  8. Operator Topologies

  9. Equivalence of Normed Linear

  Spaces

  10. Finite-Dimensional Spaces

  11. Normed Conjugate Space and

  Conjugate Operator

  Part B Hilbert Spaces

  12. Inner Product and HUbert Spaces

  13. Examples

  14. Orthogonality

  15. Orthogonal Complements and the

  Projection Theorem

  16. Orthogonal Projections

  17. Orthogonal Sets and Bases:

  Generalized Fourier Series

  18. Examples of Orthonormal Bases

  19. Unitary Operators and Equiv-

  alent Inner Product Spaces

  20. Sums and Direct Sums of

  Hilbert Spaces

  21. Continuous Linear Functionals

  Part C Special Operators

  22. The Adjoint Operator

  23. Normal and Self-Adjoint

  Operators

  24. Compact Operators

  25. Foundations of Quantum

  Mechanics

 Chapter 6 Analysis of Linear Oper-

  ators (Compact Case)

  1. Introductioa

  Part A An Illustrative Example

  2. Geometric Analysis of Operators

  3. Geometric Analysis. The Eigen-

  value-Eigenvector Problem

  4. A Finite-Dimensional Problem

  Part B The Spectrum

  5. The Spectrum of Linear

  Transformations

  6. Examples of Spectra

  7. Properties of the Spectrum

  Part C Spectral Analysis

  8. Resolutions of the Identity

  9. Weighted Sums of Projections

  10. Spectral Properties of Compact,

  Normal, and Self-Adjoint

  Operators

  11. The Spectral Theorem

  12. Functions of Operators

  (Operational Calculus)

  13. Applications of the Spectral

  Theorem

  14. Nonnormal Operators

 Chapter 7 Analysis of Unbounded

  Operators

  1. Introduction

  2. Green's Functions

  3. Symmetric Operators

  4. Examples of Symmetric

  Operators

  5. Sturmiouville Operators

  6. Ghrding's Inequality

  7. EUiptie Partial Differential

  Operators

  8. The Dirichlet Problem

  9. The Heat Equation and Wave

  Equation

  10. Self-Adjoint Operators

  11. The Cayley Transform

  12. Quantum Mechanics, Revisited

  13. Heisenberg Uncertainty Principle

  14. The Harmonic Oscillator

  Appendix ,4 The H61der, Schwartz,

  and Minkowski

  Inequalities

  Appendix B Cardinality

  Appendix C Zom's temnm

  Appendix D Integration and

  Measure Theory

  1. Introduction

  2. The Riemann Integral

  3. A Problem with the Riemann

  Integral

  4. The Space Co

  5. Null Sets

  6. Convergence Almost Everywhere

  7. The Lebesgue Integral

  8. Limit Theorems

  9. Miscellany

  10. Other Definitions of the Integral

  11. The Lebesgue Spaces,

  12. Dense Subspaees of

  13. Differentiation

  14. The Radon-Nikodym Theorem

  15. Fubini Theorem

  Appendix E Probability Spaces and

  Stochastic Processes

  1. Probability Spaces

  2. Random Variables and

  Probability Distributions

  3. Expectation

  4. Stochastic Independence

  5. Conditional Expectation Operator

  6. Stochastic Processes

  Index of Symbols

  Index