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E-raamat: Geometric Applications of Fourier Series and Spherical Harmonics

(University of Arizona)
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Geometric Applications of Fourier Series and Spherical HarmonicsSuurem pilt
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A full exposition of the classical theory of spherical harmonics and their use in proving stability results.

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.

Arvustused

Review of the hardback: ' these geometric results appear here in book form for the first time developed as concretely as possible, with full proofs.' L'Enseignement Mathématique Review of the hardback: 'Of the two main approaches to convex sets, the analytic is comprehensively covered by this welcome book.' Mathematika

Muu info

A full exposition of the classical theory of spherical harmonics and their use in proving stability results.
1. Analytic preparations
2. Geometric preparations
3. Fourier series and spherical harmonics
4. Geometric applications of Fourier series
5. Geometric applications of spherical harmonics.
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