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OverviewThe 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. Full Product DetailsAuthor: Alexander Koldobsky , Yaskin VladyslavPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: illustrated edition Volume: No. 108 Weight: 0.225kg ISBN: 9780821844564ISBN 10: 0821844563 Pages: 107 Publication Date: 30 December 2007 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsHyperplane sections of $\ell_p$-balls Volume and the Fourier transform Intesection bodies The Busemann-Petty problem Projections and the Fourier transform Intersection bodies and $L_p$-spaces On the road between polar projecltion bodies and intersection bodies Open problems Bibliography Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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