- 工程与科学中的线性算子理论(英文版)
- - 作者：(美)内勒//塞尔
  - 出版社：世界图书出版公司
  - ISBN：9787510095566
  - 出版日期：2015/05/01
  - 页数：624
- 售价：39.2

内容大纲
作者介绍
目录
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

内容大纲

作者介绍

目录

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