The interface between convex geometry and harmonic analysis
著者
書誌事項
The interface between convex geometry and harmonic analysis
（Regional conference series in mathematics, no. 108）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society with support from the National Science Foundation, c2008
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注記
"This text arises from ten lectures given by the first-named author at the NSF/CBMS conference 'The Interface between Convex Geometry and Harmonic Analysis' held on July 29-August 3, 2006 at Kansas State University in Manhattan, KS."--Pref
Includes bibliographical references (p. 101-105) and index
内容説明・目次
内容説明
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.
目次
Hyperplane 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.
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