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Basic Operator Theory / Edition 1

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Overview

Basic Operator Theory provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential and integral equations, approximation theory, and numerical analysis. A textbook designed for senior undergraduate and graduate students, Basic Operator Theory begins with the geometry of Hilbert space and proceeds to the spectral theory for compact self-adjoint operators with a wide range of applications. Part of the volume is devoted to Banach spaces and operators acting on these spaces.

Presented as a natural continuation of linear algebra, Basic Operator Theory provides a firm foundation in operator theory, an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.

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Product Details

  • ISBN-13: 9780817630287
  • Publisher: Birkhauser Verlag
  • Publication date: 1/1/1981
  • Edition description: 2001
  • Edition number: 1
  • Pages: 304
  • Product dimensions: 0.64 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

Introduction
• I. Hilbert Spaces
• II. Bounded Linear Operators on Hilbert Spaces
• III. Spectral Theory of Compact Self Adjoint Operators
• IV. Spectral Theory of Integral Operators
• V. Oscillations of an Elastic String
• VI. Operational Calculus with Applications
• VII. Solving Linear Equations by Iterative Methods
• VIII. Further Developments of the Spectral Theorem
• IX. Banach Spaces
• X. Linear Operators on a Banach Space
• XI. Compact Operators on a Banach Space
• XII. Non-Linear Operators
• Appendix 1. Countable Sets and Separable Hilbert Spaces
• Appendix 2. Lebesgue Integration and LP Spaces
• Appendix 3. Proof of the Hahn-Banach Theorem
• Appendix 4. Proof of the Closed Graph Theorem
• Suggested Reading
• References
• Index

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