UID:
almahu_9947366615102882
Umfang:
1 online resource (403 p.)
ISBN:
1-282-28874-1
,
9786612288746
,
0-08-095654-8
Serie:
Mathematics in science and engineering ; no. 146
Inhalt:
Applications of functional analysis and operator theory
Anmerkung:
Description based upon print version of record.
,
Front Cover; Applications of Functional Analysis and Operator Theory; Copyright Page; Contents; Preface; Acknowledgements; Chapter 1. Banach Spaces; 1.1 Introduction; 1.2 Vector Spaces; 1.3 Normed Vector Spaces; 1.4 Banach Spaces; 1.5 Hilbert Space; Problems; Chapter 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 Spases; 2.6 Applications; Problems; Chapter 3. Foundations of Linear Operator Theory; 3.1 Introduction; 3.2 The Basic Terminology of Operator Theory
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3.3 Some Algebraic Properties of Linear Operators3.4 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; Chapter 4. Introduction to Nonlinear Operators; 4.1 Introduction; 4.2 Preliminaries; 4.3 The Contraction Mapping Principle; 4.4 The Fréchet Derivative; 4.5 Newton's Method for Nonlinear Operators; Problems; Chapter 5. Compact Sets in Banach Spaces; 5.1 Introduction; 5.2 Definitions
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5.3 Some Consequences of Compactness5.4 Some Important Compact Sets of Functions; Problems; Chapter 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; Chapter 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
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7.6 The Numerical Solution of Linear Integral EquationsProblems; Chapter 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; Chapter 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
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Chapter 10. Generalized Eigenfunction Expansions Associated with Ordinary Differential Equations10.1 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; Chapter 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
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11.5 A Fredholm Alternative for the Generalized Dirichlet Problem
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English
Weitere Ausg.:
ISBN 0-12-363260-9
Sprache:
Englisch
