Geometric Applications of Fourier Series and Spherical HarmonicsThis 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. |
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Contents
1 Analytic Preparations | 1 |
2 Geometric Preparations | 17 |
3 Fourier Series and Spherical Harmonics | 60 |
4 Geometric Applications of Fourier Series | 133 |
5 Geometric Applications of Spherical Harmonics | 181 |
| 311 | |
List of Symbols | 319 |
| 323 | |
| 326 | |
Other editions - View all
Geometric Applications of Fourier Series and Spherical Harmonics Helmut Groemer No preview available - 2009 |
Common terms and phrases
already angle appear applications assumed assumption ball boundary called centered coefficients conceming condition consequence consider constant contains continuous function convergence convex body convex domain Corollary corresponding deduce defined definition denote depend derived determined differentiable dimension direction equality equation estimate example exists expansion expressed fact finds first follows formula Fourier series function h further Furthermore geometric given Hence holds immediately implies important inequality integral kind Legendre Lemma length mean measure mentioned metric observing obtain obvious orthogonal particular polygons polynomials possible present projection proof Proposition prove References regarding relation Remarks respect restriction rotor satisfied SCHNEIDER Sd_1 sequence shown shows smoothness spherical harmonics stability star body statement Steiner support function symmetric Theorem transformation values vectors volume width write written yields
Bibliographic information
| Title | Geometric Applications of Fourier Series and Spherical Harmonics Volume 61 of Encyclopedia of Mathematics and its Applications, ISSN 0953-4806 |
| Author | Helmut Groemer |
| Editor | G. C. Rota |
| Contributors | Cambridge University Press, B. Doran, P. Flajolet, M. Ismail, T. Y. Lam, E. Lutwak |
| Edition | illustrated, reprint |
| Publisher | Cambridge University Press, 1996 |
| ISBN | 0521473187, 9780521473187 |
| Length | 329 pages |
| Subjects | › › Mathematics / Differential Equations / General Mathematics / Functional Analysis Mathematics / Infinity Mathematics / Mathematical Analysis |
| Export Citation | BiBTeX EndNote RefMan |