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The Interface Between Convex Geometry and Harmonic Analysis - 9780821844564

Un libro in lingua di Alexander Koldobsky Vladyslav Yaskin edito da Amer Mathematical Society, 2008

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Central to geometry and particularly useful in applications to other areas of mathematics as well, this aspect of study of convex bodies and the geometry of sections has been advanced by methods from Fourier analysis, the idea being to express certain properties of bodies in terms of the Fourier transform and then to use methods of Fourier analysis to solve geometric problems. Developed from material presented at the conference of the same name held July and August 2006 at Kansas State U. in Manhattan, Kansas, this is written in the form of lectures accessible to graduate students and contains information on the newest advances. It covers hyper-plane sections of lp-balls, volume and the Fourier transform, intersection bodies, the Busemann-Petty problem, projections and the Fourier transform, intersection bodies and Lp-spaces, between polar projection bodies and intersection bodies, and open problems. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)

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