| Geometric Applications of Fourier Series and Spherical Harmonics Contributor(s): Groemer, Helmut (Author) |
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ISBN: 0521473187 ISBN-13: 9780521473187 Publisher: Cambridge University Press OUR PRICE: $134.90 Product Type: Hardcover - Other Formats Published: September 1996 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Infinity - Mathematics | Mathematical Analysis - Mathematics | Probability & Statistics - General |
| Dewey: 515.243 |
| LCCN: 95025363 |
| Series: Encyclopedia of Mathematics and Its Applications |
| Physical Information: 1" H x 6.53" W x 9.59" (1.51 lbs) 344 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |