On an analytic generalization of the Busemann-Petty problem

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Abstract

In this paper, we establish an extension of the connections between an analytic generalization of the Busemann-Petty problem and the positive definite distributions. Our results show that the structure of the positive definite distributions in Rn is closely related to the analytic generalization of the Busemann-Petty problem which was posed by Koldobsky. © 2007 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Dual mixed volume
  • Fourier transform
  • Parallel section function
  • Star body

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Authors

  • Songjun Lv

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