Book:Georgi E. Shilov/Elementary Functional Analysis
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Georgi E. Shilov: Elementary Functional Analysis
Published $\text {1996}$, 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