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  3. Geometric Applications of Fourier Series and Spherical Harmonics
  • Cited by 203
Publisher:
Cambridge University Press
Online publication date:
September 2009
Print publication year:
1996
Online ISBN:
9780511530005
DOI:
https://doi.org/10.1017/CBO9780511530005
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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