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FOURIER TRANSFORM AND Lp-MIXED PROJECTION BODIES

  • Liu, Lijuan (SCHOOL OF MATHEMATICS AND COMPUTATIONAL SCIENCE HUNAN UNIVERSITY OF SCIENCE AND TECHNOLOGY) ;
  • Wang, Wei (SCHOOL OF MATHEMATICS AND COMPUTATIONAL SCIENCE HUNAN UNIVERSITY OF SCIENCE AND TECHNOLOGY) ;
  • He, Binwu (DEPARTMENT OF MATHEMATICS SHANGHAI UNIVERSITY)
  • Received : 2009.04.01
  • Accepted : 2009.11.03
  • Published : 2010.09.30

Abstract

In this paper we define the $L_p$-mixed curvature function of a convex body. We develop a formula connection the support function of $L_p$-mixed projection body with Fourier transform of the $L_p$-mixed curvature function. Using this formula we solve an analog of the Shephard projection problem for $L_p$-mixed projection bodies.

Acknowledgement

Supported by : National Natural Science Foundation of China, Shanghai University

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