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Basic Classes of Linear Operators~tqw~ darksiderg

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Basic Classes of Linear Operators
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Type.................: Ebook
Part Size............: 11,753,176 bytes




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Posted by............: ~tqw~

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Release Notes
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This book provides an introduction to functional analysis with an emphasis on
the theory of linear operators and its application to differential equations,
integral equations, infinite systems of linear equations, approximation theory,
and numerical analysis. As textbook designed for senior undergraduate and
graduate students, it begins with the geometry of Hilbert spaces and proceeds to
the theory of linear operators on these spaces including Banach spaces.
Presented as a natural continuation of linear algebra, the book provides a firm
foundation in operator theory which is an essential part of mathematical
training for students of mathematics, engineering, and other technical sciences.

Table of Contents

Preface
Introduction
Ch. I Hilbert Spaces 1
Ch. II Bounded Linear Operators on Hilbert Spaces 51
Ch. III Laurent and Toeplitz Operators on Hilbert Spaces 135
Ch. IV Spectral Theory of Compact Self Adjoint Operators 171
Ch. V Spectral Theory of Integral Operators 193
Ch. VI Unbounded Operators on Hilbert Space 203
Ch. VII Oscillations of an Elastic String 219
Ch. VIII Operational Calculus with Applications 225
Ch. IX Solving Linear Equations by Iterative Methods 237
Ch. X Further Developments of the Spectral Theorem 243
Ch. XI Banach Spaces 259
Ch. XII Linear Operators on a Banach Space 277
Ch. XIII Compact Operators on a Banach Space 299
Ch. XIV Poincare Operators: Determinant and Trace 317
Ch. XV Fredholm Operators 347
Ch. XVI Toeplitz and Singular Integral Operators 361
Ch. XVII Non Linear Operators 401
App. 1 Countable sets and Separable Hilbert Spaces 409
App. 2 The Lebesgue integral and L[subscript p] Spaces 411
Suggested Reading 415
References 417
List of Symbols 419
Index 421

Product Details

* ISBN: 3764369302
* ISBN-13: 9783764369309
* Format: Paperback, 423pp
* Publisher: Birkhauser Verlag
* Pub. Date: September 2003

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