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  3. Geometric Applications of Fourier Series and Spherical Harmonics
  • Cited by 216
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    • Publisher:
      Cambridge University Press
      Publication date:
      September 2009
      September 1996
      ISBN:
      9780511530005
      9780521473187
      9780521119658
      DOI:
      https://doi.org/10.1017/CBO9780511530005
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.682kg, 344 Pages
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.48kg, 344 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Number Theory
      Series:
      Encyclopedia of Mathematics and its Applications (61)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Number Theory
    Series:
    Encyclopedia of Mathematics and its Applications (61)
    Information

    Book description

    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.

    Reviews

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

    Source: L’Enseignement Mathématique

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

    Source: Mathematika

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