Geometric Applications of Fourier Series and Spherical Harmonics

Geometric Applications of Fourier Series and Spherical Harmonics

by Helmut Groemer
     
 

ISBN-10: 0521119650

ISBN-13: 9780521119658

Pub. Date: 09/17/2009

Publisher: Cambridge University Press

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…  See more details below

Overview

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.

Product Details

ISBN-13:
9780521119658
Publisher:
Cambridge University Press
Publication date:
09/17/2009
Series:
Encyclopedia of Mathematics and its Applications Series, #61
Pages:
344
Product dimensions:
6.14(w) x 9.21(h) x 0.71(d)

Table of Contents

Preface
1Analytic Preparations1
2Geometric Preparations17
3Fourier Series and Spherical Harmonics60
4Geometric Applications of Fourier Series133
5Geometric Applications of Spherical Harmonics181
References311
List of Symbols319
Author Index323
Subject Index326

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