An Introduction to Hilbert Space / Edition 1

by N. Young

Overview

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.

Product Details

ISBN-13:	9780521337175
Publisher:	Cambridge University Press
Publication date:	07/21/1988
Series:	Cambridge Mathematical Textbooks Series
Edition description:	New Edition
Pages:	250
Product dimensions:	5.98(w) x 9.02(h) x 0.59(d)

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.

What People are Saying About This

From the Publisher

"...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

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

From the Publisher