Fourier transform and $L_{p}$-mixed projection bodies
Bull. Korean Math. Soc. 2010 Vol. 47, No. 5, 1011-1023
https://doi.org/10.4134/BKMS.2010.47.5.1011
Published online September 1, 2010
Lijuan Liu, Wei Wang, and Binwu He
Hunan University of Science and Technology, Hunan University of Science and Technology, Shanghai University
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.
Keywords : Fourier transform, $L_{p}$-mixed curvature function, $L_{p}$-mixed projection body
MSC numbers : 52A40, 52A20
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