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The Interface Between Convex Geometry and Harmonic Analysis (CBMS Regional Conference Series in Mathematics) - Softcover

American Mathematical Society

 
9780821844564: The Interface Between Convex Geometry and Harmonic Analysis (CBMS Regional Conference Series in Mathematics)
Softcover
ISBN 10: 0821844563 ISBN 13: 9780821844564
Publisher: American Mathematical Society, 2008

Synopsis

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.

"synopsis" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2008
Language
English
ISBN 10 
0821844563
ISBN 13 
9780821844564
Binding
Paperback
Number of pages
105