I: Functional Analysis

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Gulf Professional Publishing, 1980 - Science - 400 pages
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This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.
 

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Contents

Chapter I PRELIMINARIES
1
Chapter II HILBERT SPACES
36
Chapter III BANACH SPACES
67
Chapter IV TOPOLOGICAL SPACES
90
Chapter V LOCALLY CONVEX SPACES
124
Chapter VI BOUNDED OPERATORS
182
Chapter VII THE SPECTRAL THEOREM
221
Chapter VIII UNBOUNDED OPERATORS
249
THE FOURIER TRANSFORM
318
SUPPLEMENTARY MATERIAL
344
List of Symbols
393
Index
395
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