Geometric & Functional Analysis GAFA

, Volume 10, Issue 6, pp 1507–1526

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 Lp-spaces. These connections lead to generalizations of the recent solution to the Busemann—Petty problem on sections of convex bodies.

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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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