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Introduction to Hilbert Space

ISBN-10: 0521337178

ISBN-13: 9780521337175

Edition: 1988

Authors: N. Young

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Description:

This textbook is an introduction to the theory of Hilbert spaces and its applications. The notion of a Hilbert space is a central idea in functional analysis and can be used in numerous branches of pure and applied mathematics. Dr. Young stresses these applications particularly for the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. The book is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). The book will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.
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Book details

Copyright year: 1988
Publisher: Cambridge University Press
Publication date: 7/21/1988
Binding: Paperback
Pages: 250
Size: 5.75" wide x 9.00" long x 0.50" tall
Weight: 0.748
Language: English

Foreword
Introduction
Inner product spaces
Normed spaces
Hilbert and Banach spaces
Orthogonal expansions
Classical Fourier series
Dual spaces
Linear operators
Compact operators
Sturm-Liouville systems
Green's functions
Eigenfunction expansions
Positive operators and contractions
Hardy spaces
Interlude: complex analysis and operators in engineering
Approximation by analytic functions
Approximation by meromorphic functions
Appendix
References
Answers to selected problems
Afterword
Index of notation
Subject index