An Introduction to Hilbert Space
An Introduction to Hilbert Space
CAD$109.95
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.
Reviews & endorsements
"...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
Product details
July 1988Paperback
9780521337175
250 pages
229 × 152 × 15 mm
0.41kg
Available
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.
