The Interface Between Convex Geometry and Harmonic Analysis - Couverture souple

American Mathematical Society

Couverture souple

ISBN 10 : 0821844563 ISBN 13 : 9780821844564

Editeur : American Mathematical Society, 2007

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2007
• Langue: anglais
• ISBN 10: 0821844563
• ISBN 13: 9780821844564
• Reliure: Broché
• Nombre de pages: 105
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible