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Geometric Applications of Fourier Series and Spherical Harmonics

$71.99 (C)

Part of Encyclopedia of Mathematics and its Applications

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

$ 71.99 (C)
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About the Authors
  • This is the first comprehensive exposition of the application of spherical harmonics to prove geometric results. The author presents all the necessary tools from classical theory of spherical harmonics with full proofs. Groemer uses these tools to prove geometric inequalities, uniqueness results for projections and intersection by planes or half-spaces, stability results, and characterizations of convex bodies of a particular type, such as rotors in convex polytopes. Results arising from these analytical techniques have proved useful in many applications, particularly those related to stereology. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets.

    •  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

    "The author's attention to detail and insistence on complete proofs make this book an excellent resource. In addition to the selected major results, each section closes with notes which provide the historical background and references to, and discussion of, other related results. This is indeed a comprehensive presentation of the subject matter with much to offer both the beginner and the expert." Paul Goodey, Mathematical Reviews

    "The author's attention to detail and insistence on complete proofs make this book an excellent resource. In addition to the selected major results, each section closes with notes which provide the historical background and references to, and discussion of other realted results. This is indeed a comprehensive presentation of the subject matter with much to offer both to the beginner and the expert." P.R. Goodey, Mathematical Reviews

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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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