Geometric Applications of Fourier Series and Spherical Harmonics

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Overview

This is the first comprehensive exposition of the application of spherical harmonics to prove geometric results. The author presents all the necessary tools from classical theory of spherical harmonics with full proofs. Groemer uses these tools to prove geometric inequalities, uniqueness results for projections and intersection by planes or half-spaces, stability results, and characterizations of convex bodies of a particular type, such as rotors in convex polytopes. Results arising from these analytical techniques have proved useful in many applications, particularly those related to stereology. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets.

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Editorial Reviews

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"The author's attention to detail and insistence on complete proofs make this book an excellent resource. In addition to the selected major results, each section closes with notes which provide the historical background and references to, and discussion of, other related results. This is indeed a comprehensive presentation of the subject matter with much to offer both the beginner and the expert." Paul Goodey, Mathematical Reviews

"The author's attention to detail and insistence on complete proofs make this book an excellent resource. In addition to the selected major results, each section closes with notes which provide the historical background and references to, and discussion of other realted results. This is indeed a comprehensive presentation of the subject matter with much to offer both to the beginner and the expert." P.R. Goodey, Mathematical Reviews

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Product Details

Table of Contents

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.

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