An Introduction to Hilbert Space

This textbook is an introduction to the theory of Hilbert space and its applications.

N. Young (Author)

9780521337175, Cambridge University Press

Paperback, published 21 July 1988

250 pages
22.9 x 15.2 x 1.5 cm, 0.41 kg

' … the author's style is a delight. Each topic is carefully motivated and succinctly presented, and the exposition is enthusiastic and limpid … Young has done a really fine job in presenting a subject of great mathematical elegance as well as genuine utility, and I recommend it heartily.' The Times Higher Education Supplement

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]