Elementary Functional Analysis

Overview

Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms — including problems in the complex domain, especially involving the Laplace transform — and more. Each chapter includes a set of problems, with hints and answers. Bibliography. 1974 edition.

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Elementary Functional Analysis

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Overview

Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms — including problems in the complex domain, especially involving the Laplace transform — and more. Each chapter includes a set of problems, with hints and answers. Bibliography. 1974 edition.

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Editorial Reviews

Booknews
**** Reprint of the MIT Press original of 1974 (which is honored by inclusion in BCL3. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780486689234
  • Publisher: Dover Publications
  • Publication date: 1/18/1996
  • Series: Dover Books on Mathematics Series
  • Edition description: REVISED
  • Edition number: 2
  • Pages: 352
  • Product dimensions: 5.37 (w) x 8.44 (h) x 0.67 (d)

Table of 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 of 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
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