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Geometric Applications of Fourier Series and Spherical Harmonics

£52.99

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: September 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521119658

£ 52.99
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  • This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.

    •  Offers a detailed and self-contained presentation of the theory of spherical harmonics
    • Important supplement to books by Schneider and Gardner in the same series
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    Reviews & endorsements

    Review of the hardback: '… these geometric results appear here in book form for the first time … developed as concretely as possible, with full proofs.' L'Enseignement Mathématique

    Review of the hardback: 'Of the two main approaches to convex sets, the analytic is comprehensively covered by this welcome book.' Mathematika

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    Product details

    • Date Published: September 2009
    • format: Paperback
    • isbn: 9780521119658
    • length: 344 pages
    • dimensions: 234 x 156 x 18 mm
    • weight: 0.48kg
    • availability: Available
  • Table of Contents

    Preface
    1. Analytic preparations
    2. Geometric preparations
    3. Fourier series and spherical harmonics
    4. Geometric applications of Fourier series
    5. Geometric applications of spherical harmonics
    References
    List of symbols
    Author index
    Subject index.

  • Author

    Helmut Groemer, University of Arizona

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