Geometric Applications of Fourier Series and Spherical Harmonics

A full exposition of the classical theory of spherical harmonics and their use in proving stability results.

Helmut Groemer (Author)

9780521119658, Cambridge University Press

Paperback, published 17 September 2009

344 pages
23.4 x 15.6 x 1.8 cm, 0.48 kg

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

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.

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.

Subject Areas: Functional analysis & transforms [PBKF]