An Introduction to Hilbert Space

by N. Young

Overview

This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to 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. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it 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.

Product Details

ISBN-13:	9781107713031
Publisher:	Cambridge University Press
Publication date:	07/21/1988
Sold by:	Barnes & Noble
Format:	eBook
File size:	17 MB
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Table of Contents

Foreword; Introduction; 1. Inner product spaces; 2. Normed spaces; 3. Hilbert and Banach spaces; 4. Orthogonal expansions; 5. Classical Fourier series; 6. Dual spaces; 7. Linear operators; 8. Compact operators; 9. Sturm-Liouville systems; 10. Green's functions; 11. Eigenfunction expansions; 12. Positive operators and contractions; 13. Hardy spaces; 14. Interlude: complex analysis and operators in engineering; 15. Approximation by analytic functions; 16. Approximation by meromorphic functions; Appendix; References; Answers to selected problems; Afterword; Index of notation; Subject index.

Editorial Reviews

"...presents a very clear and elegant exposition of the basic notions of the theory of Hilbert space...It is beautiful and relatively recent mathematics..." Mathematical Reviews

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