Geometric Applications of Fourier Series and Spherical Harmonics (Encyclopedia of Mathematics and its Applications)

H. Groemer

ISBN 10: 0521473187 / ISBN 13: 9780521473187

Published by Cambridge University Press, 1996

About this Item

Type: Book N.B. Small plain label to ffep.

Seller Inventory # 051808

Bibliographic Details

• Title: Geometric Applications of Fourier Series and Spherical Harmonics (Encyclopedia of Mathematics and its Applications)
• Publisher: Cambridge University Press
• Publication Date: 1996
• Language: English
• ISBN 10: 0521473187
• ISBN 13: 9780521473187
• Binding: Cloth
• Condition: Very Good
• Dust Jacket Condition: Very Good
• Weight: 27 ounces
• Seller catalogs:
  • MATHEMATICS

About this title

Synopsis

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.

From the Back Cover

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.