دانلود کتاب Functional Analysis: A Terse Introduction

فهرست مطالب :

Contents\nList of Figures\nBasic Notation\n1 Choice Principles\n 1.1 Axiom of Choice\n 1.2 Some Applications\n 1.3 Problems\n2 Hilbert Spaces\n 2.1 Norms\n 2.2 Inner Products and Hilbert Spaces\n 2.3 Some Geometric Properties\n 2.4 Orthogonality\n 2.5 Orthogonal Sequences\n 2.6 Problems\n3 Completeness, Completion and Dimension\n 3.1 Banach Spaces\n 3.2 Completion and Dimension\n 3.3 Separability\n 3.4 Problems\n4 Linear Operators\n 4.1 Linear Transformations\n 4.2 Back to Matrices\n 4.3 Boundedness\n 4.4 Problems\n5 Functionals and Dual Spaces\n 5.1 A Special Type of Linear Operators\n 5.2 Dual Spaces\n 5.3 The Bra-ket Notation\n 5.4 Problems\n6 Fourier Series\n 6.1 The Space L2[–0, 0]\n 6.2 Convergence Conditions for the Fourier Series\n 6.2.1 Sufficient Convergence Conditions for the Fourier Series in a Point\n 6.2.2 Conditions for Uniform Convergence for the Fourier Series\n 6.3 Problems\n7 Fourier Transform\n 7.1 Convolution\n 7.2 L1 Theory\n 7.3 L2 Theory\n 7.4 Schwartz Class\n 7.5 Problems\n8 Fixed Point Theorem\n 8.1 Some Applications\n 8.1.1 Neumann Series\n 8.1.2 Differential Equations\n 8.1.3 Integral Equations\n 8.1.4 Fractals\n 8.2 Problems\n9 Baire Category Theorem\n 9.1 Baire Categories\n 9.2 Baire Category Theorem\n 9.3 Problems\n10 Uniform Boundedness Principle\n 10.1 Problems\n11 Open Mapping Theorem\n 11.1 Problems\n12 Closed Graph Theorem\n 12.1 Problems\n13 Hahn–Banach Theorem\n 13.1 Extension Theorems\n 13.2 Minkowski Functional\n 13.3 Separation Theorem\n 13.4 Applications of the Hahn–Banach Theorem\n 13.5 Problems\n14 The Adjoint Operator\n 14.1 Hilbert Spaces\n 14.2 Banach Spaces\n 14.3 Problems\n15 Weak Topologies and Reflexivity\n 15.1 Weak* Topology\n 15.2 Reflexive Spaces\n 15.3 Problems\n16 Operators in Hilbert Spaces\n 16.1 Compact Operators\n 16.2 Normal and Self-Adjoint Operators\n 16.3 Problems\n17 Spectral Theory of Operators on Hilbert Spaces\n 17.1 A Quick Review of Spectral Theory in Finite Dimensions\n 17.2 The Spectral Theorem for Compact Self-Adjoint Operators\n 17.3 Problems\n18 Compactness\n 18.1 Metric Spaces\n 18.2 Compactness in Some Function Spaces\n 18.2.1 Space l2\n 18.2.2 Space of Continuous Functions\n 18.2.3 Lebesgue Spaces\n 18.3 Problems\nBibliography\nIndex