Book:Georgi E. Shilov/Elementary Functional Analysis

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Georgi E. Shilov: Elementary Functional Analysis

Published $1996$, Dover

ISBN 978-0486689234.




Subject Matter


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