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Geometric & Functional Analysis GAFA

, Volume 10, Issue 6, pp 1507–1526 | Cite as

A functional analytic approach to intersection bodies

  • A. Koldobsky

Abstract.

We consider several generalizations of the concept of an intersection body and show their connections with the Fourier transform and embeddings in L p -spaces. These connections lead to generalizations of the recent solution to the Busemann—Petty problem on sections of convex bodies.

Keywords

Analytic Approach Convex Body Intersection Body Recent Solution Functional Analytic Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • A. Koldobsky
    • 1
  1. 1.Department of Mathematics, University of Missouri-Columbia, Columbia MO 65211, USA, e-mail: koldobsk@math.missouri.eduUS

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