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: 9780817642624
  • Publisher: Birkhauser Verlag
  • Publication date: 7/27/2001
  • Edition description: 1st ed. 1981. 1st softcover printing 2001
  • Edition number: 1
  • Pages: 304
  • Product dimensions: 0.64 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Introduction
Ch. I Hilbert Spaces 1
Ch. II Bounded Linear Operators on Hilbert Spaces 51
Ch. III Spectral Theory of Compact Self Adjoint Operators 105
Ch. IV Spectral Theory of Integral Operators 131
Ch. V Oscillations of an Elastic String 153
Ch. VI Operational Calculus with Applications 159
Ch. VII Solving Linear Equations by Iterative Methods 173
Ch. VIII Further Developments of the Spectral Theorem 181
Ch. IX Banach Spaces 193
Ch. X Linear Operators on a Banach Space 211
Ch. XI Compact Operators on a Banach Spaces 237
Ch. XII Non Linear Operators 255
App. 1 Countable Sets and Separable Hilbert Spaces 265
App. 2 Lebesgue Integration and L[subscript P] Spaces 267
App. 3 Proof of the Hahn-Banach Theorem 273
App. 4 Proof of the Closed Graph Theorem 277
Suggested Reading 280
References 281
Index 282
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