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

Helmut Groemer (Author)

Book Description

Publication Date: September 13, 1996 | ISBN-10: 0521473187 | ISBN-13: 978-0521473187

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.

Editorial Reviews

Review

"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

Book Description

This self-contained, comprehensive treatise presents a careful introduction to the classical theory of spherical harmonics and shows how this theory can be used to prove geometric results such as geometric inequalities, uniqueness results for projections and intersection by hyperplanes or half-spaces, and stability. The analytic nature of the proofs is emphasized, since this makes them particularly useful in applications. Many of the results appear here in book form for the first time. This reference will be welcomed by both pure and applied mathematicians.

Product Details

• Hardcover: 344 pages
• Publisher: Cambridge University Press (September 13, 1996)
• Language: English
• ISBN-10: 0521473187
• ISBN-13: 978-0521473187
• Product Dimensions: 9.6 x 6.5 x 1 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #3,255,159 in Books (See Top 100 in Books)

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