Geometric Applications of Fourier Series and Spherical Harmonics

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Cambridge University Press, Sep 13, 1996 - Mathematics - 329 pages
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. Almost all these geometric results appear here in book form for the first time. An important feature of the book is that all the necessary tools from classical theory of spherical harmonics are developed as concretely as possible, 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 characterizations 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 mathematicians.
 

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Contents

1 Analytic Preparations
1
2 Geometric Preparations
17
3 Fourier Series and Spherical Harmonics
60
4 Geometric Applications of Fourier Series
133
5 Geometric Applications of Spherical Harmonics
181
References
311
List of Symbols
319
Author Index
323
Subject Index
326
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