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An Introduction to Hilbert Space

An Introduction to Hilbert Space

textbook
  • Date Published: July 1988
  • availability: Available
  • format: Paperback
  • isbn: 9780521337175

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  • 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

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    Product details

    • Date Published: July 1988
    • format: Paperback
    • isbn: 9780521337175
    • length: 250 pages
    • dimensions: 229 x 152 x 15 mm
    • weight: 0.41kg
    • availability: 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.

  • Instructors have used or reviewed this title for the following courses

    • Functional Analysis
  • Author

    N. Young

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