Interface Between Convex Geometry and Harmonic Analysis
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A01=American Mathematical Society
Author_American Mathematical Society
Category=PBK
Category=PBM
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Product details
- ISBN 9780821844564
- Weight: 225g
- Publication Date: 30 Dec 2007
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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The study of convex bodies is a central part of geometry, and is particularly useful in applications to other areas of mathematics and the sciences. Recently, methods from Fourier analysis have been developed that greatly improve our understanding of the geometry of sections and projections of convex bodies. The idea of this approach is to express certain properties of bodies in terms of the Fourier transform and then to use methods of Fourier analysis to solve geometric problems. The results covered in the book include an analytic solution to the Busemann-Petty problem, which asks whether bodies with smaller areas of central hyperplane sections necessarily have smaller volume, characterizations of intersection bodies, extremal sections of certain classes of bodies, and a Fourier analytic solution to Shephard's problem on projections of convex bodies.
