Applications of functional analysis and operator theory.

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Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Hutson, V.
Otros Autores: Pym, J. S. (John Sydney), 1938-, Cloud, Michael J.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; Boston : Elsevier, 2005.
Edición:2nd ed. /
Colección:Mathematics in science and engineering ; v. 200.
Temas:
Functional analysis.
Operator theory.
Analyse fonctionnelle.
Th�eorie des op�erateurs.
MATHEMATICS > Functional Analysis.
Functional analysis
Operator theory
Acceso en línea:Texto completo
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Tabla de Contenidos:
  • Preface.
  • Acknowledgements.
  • Contents.
  • 1. Banach Spaces
  • 1.1 Introduction
  • 1.2 Vector Spaces
  • 1.3 Normed Vector Spaces
  • 1.4 Banach Spaces
  • 1.5 Hilbert Space
  • Problems
  • 2. Lebesgue Integration and the Lp Spaces
  • 2.1 Introduction
  • 2.2 The Measure of a Set
  • 2.3 Measurable Functions
  • 2.4 Integration
  • 2.5 The Lp Spaces
  • 2.6 Applications
  • Problems
  • 3. Foundations of Linear Operator Theory
  • 3.1 Introduction
  • 3.2 The Basic Terminology of Operator Theory
  • 3.3 Some Algebraic Properties of Linear Operators
  • 3.4 Continuity and Boundedness
  • 3.5 Some Fundamental Properties of Bounded Operators
  • 3.6 First Results on the Solution of the Equation Lf=g
  • 3.7 Introduction to Spectral Theory
  • 3.8 Closed Operators and Differential Equations
  • Problems
  • 4. Introduction to Nonlinear Operators
  • 4.1 Introduction
  • 4.2 Preliminaries
  • 4.3 The Contraction Mapping Principle
  • 4.4 The Frechet Derivative
  • 4.5 Newton's Method for Nonlinear Operators
  • Problems
  • 5. Compact Sets in Banach Spaces
  • 5.1 Introduction
  • 5.2 Definitions
  • 5.3 Some Consequences of Compactness
  • 5.4 Some Important Compact Sets of Functions
  • Problems
  • 6. The Adjoint Operator
  • 6.1 Introduction
  • 6.2 The Dual of a Banach Space
  • 6.3 Weak Convergence
  • 6.4 Hilbert Space
  • 6.5 The Adjoint of a Bounded Linear Operator
  • 6.6 Bounded Self-adjoint Operators
  • Spectral Theory
  • 6.7 The Adjoint of an Unbounded Linear Operator in Hilbert Space
  • Problems
  • 7. Linear Compact Operators
  • 7.1 Introduction
  • 7.2 Examples of Compact Operators
  • 7.3 The Fredholm Alternative
  • 7.4 The Spectrum
  • 7.5 Compact Self-adjoint Operators
  • 7.6 The Numerical Solution of Linear Integral Equations
  • Problems
  • 8. Nonlinear Compact Operators and Monotonicity
  • 8.1 Introduction
  • 8.2 The Schauder Fixed Point Theorem
  • 8.3 Positive and Monotone Operators in Partially Ordered Banach Spaces
  • Problems
  • 9. The Spectral Theorem
  • 9.1 Introduction
  • 9.2 Preliminaries
  • 9.3 Background to the Spectral Theorem
  • 9.4 The Spectral Theorem for Bounded Self-adjoint Operators
  • 9.5 The Spectrum and the Resolvent
  • 9.6 Unbounded Self-adjoint Operators
  • 9.7 The Solution of an Evolution Equation
  • Problems
  • 10. Generalized Eigenfunction Expansions Associated with Ordinary Differential Equations
  • 10.1 Introduction
  • 10.2 Extensions of Symmetric Operators
  • 10.3 Formal Ordinary Differential Operators: Preliminaries
  • 10.4 Symmetric Operators Associated with Formal Ordinary Differential Operators
  • 10.5 The Construction of Self-adjoint Extensions
  • 10.6 Generalized Eigenfunction Expansions
  • Problems
  • 11. Linear Elliptic Partial Differential Equations
  • 11.1 Introduction
  • 11.2 Notation
  • 11.3 Weak Derivatives and Sobolev Spaces
  • 11.4 The Generalized Dirichlet Problem
  • 11.5 Fredholm Alternative for Generalized Dirichlet Problem
  • 11.6 Smoothness of Weak Solutions
  • 11.7 Further Developments
  • Problems
  • 12. The Finite Element Method
  • 12.1 Introduction
  • 12.2 The Ritz Method
  • 12.3 The Rate of Convergence of the Finite Element Method
  • Problems
  • 13. Introduction to Degree Theory
  • 13.1 Introduction
  • 13.2 The Degree in Finite Dimensions
  • 13.3 The Leray-Schauder Degree
  • 13.4 A Problem in Radiative Transfer
  • Problems
  • 14. Bifurcation Theory
  • 14.1 Introduction
  • 14.2 Local Bifurcation Theory
  • 14.3 Global Eigenfunction Theory
  • Problems
  • References
  • List of Symbols
  • Index.

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