Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2010; 47(5): 1011-1023

Printed September 1, 2010

https://doi.org/10.4134/BKMS.2010.47.5.1011

Copyright © The Korean Mathematical Society.

Fourier transform and $L_{p}$-mixed projection bodies

Lijuan Liu, Wei Wang, and Binwu He

Hunan University of Science and Technology, Hunan University of Science and Technology, Shanghai University

Abstract

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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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