IUMJ

Title: Fourier transform and Firey projections of convex bodies

Authors: Dmitry Ryabogin and Artem Zvavitch

Issue: Volume 53 (2004), Issue 3, 667-682

Abstract:

In this paper we develop a Fourier analytic approach to problems in the Brunn-Minkowski-Firey theory of convex bodies. We study the notion of Firey projections and prove a version of Aleksandrov's projection theorem. We also formulate and solve an analog of the Shephard problem for Firey projections.