# 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)
• 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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