Book:Georgi E. Shilov/Elementary Functional Analysis

Subject Matter

 * Functional Analysis

Contents
Preface


 * 1. Basic Structures of Mathematical Analysis


 * 1.1 Linear Spaces


 * 1.2 Metric Spaces


 * 1.3 Normed Linear Spaces


 * 1.4 Hilbert Spaces


 * 1.5 Approximation on a Compactum


 * 1.6 Differentiation and Integration in a Normed Linear Space


 * 1.7 Continuous Linear Operators


 * 1.8 Normed Algebras


 * 1.9 Spectral Properties of Linear Operators


 * Problems


 * 2. Differential Equations


 * 2.1 Definitions and Examples


 * 2.2 The Fixed Point Theorem


 * 2.3 Existence and Uniqueness Solutions


 * 2.4 Systems of Equations


 * 2.5 Higher-Order Equations


 * 2.6 Linear Equations and Systems


 * 2.7 The Homogeneous Linear Equation


 * 2.8 The Nonhomogeneous Linear Equation


 * Problems


 * 3. Space Curves


 * 3.1 Basic Concepts


 * 3.2 Higher Derivatives


 * 3.3 Curvature


 * 3.4 The Moving Basis


 * 3.5 The Natural Equations


 * 3.6 Helices


 * Problems


 * 4. Orthogonal Expansions


 * 4.1 Orthogonal Expansions in Hilbert Space


 * 4.2 Trigonometric Fourier Series


 * 4.3 Convergence of Fourier Series


 * 4.4 Computations with Fourier Series


 * 4.5 Divergent Fourier Series and Generalized Summation


 * 4.6 Other Orthogonal Systems


 * Problems


 * 5. The Fourier Transform


 * 5.1 The Fourier Integral and Its Inversion


 * 5.2 Further Properties of the Fourier Transform


 * 5.3 Examples and Applications


 * 5.4 The Laplace Transform


 * 5.5 Quasi-Analytic Classes of Functions


 * Problems

Hints and Answers

Bibliography

Index