Geometric Applications of Fourier Series and Spherical Harmonics

Erscheinungsjahr 1996
ISBN: 978-0-521-47318-7
Verlag: Cambridge University Press

Buch, Englisch, Band 61, 344 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 681 g

Reihe: Encyclopedia of Mathematics and its Applications

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.

Autoren/Hrsg.

Groemer, H.

Groemer, Helmut

Rota, G. -C

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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.