دانلود کتاب Functional Analysis

فهرست مطالب :

cover
1
Preface
Preface to the Second Edition
Notations
Contents
About the Author
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1 Preliminaries
1.1 Linear Spaces
1.2 Topological Spaces
1.3 Measure and Integration
References
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2 Normed Linear Spaces
2.1 The Norm Topology
2.2 Examples
2.3 Continuous Linear Transformations
2.4 Applications to Differential Equations
2.5 Exercises
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3 Hahn-Banach Theorems
3.1 Analytic Versions
3.2 Reflexivity
3.3 Geometric Versions
3.4 Vector-Valued Integration
3.5 An Application to Optimization Theory
3.6 Exercises
Reference
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4 Baire\'s Theorem and Applications
4.1 Baire\'s Theorem
4.2 Principle of Uniform Boundedness
4.3 Application to Fourier Series
4.4 The Open Mapping and Closed Graph Theorems
4.5 Annihilators
4.6 Complemented Subspaces
4.7 Unbounded Operators, Adjoints
4.8 Exercises
Reference
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5 Weak and Weak* Topologies
5.1 The Weak Topology
5.2 The Weak* Topology
5.3 Reflexive Spaces
5.4 Separable Spaces
5.5 Uniformly Convex Spaces
5.6 Application: Calculus of Variations
5.7 Exercises
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6 Lp Spaces
6.1 Basic Properties
6.2 Duals of Lp Spaces
6.3 The Spaces Lp(Ω)
6.4 The Spaces W1,p(a,b)
6.5 Exercises
References
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7 Hilbert Spaces
7.1 Basic Properties
7.2 The Dual of a Hilbert Space
7.3 Application: Variational Inequalities
7.4 Orthonormal Sets
7.5 Exercises
References
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8 Compact Operators
8.1 Basic Properties
8.2 Riesz-Fredhölm Theory
8.3 Spectrum of an Operator
8.4 Spectrum of a Compact Operator
8.5 Compact Self-adjoint Operators
8.6 Exercises
References
1 (1)
Index