Fourier transform and Firey projections of convex bodies Dmitry RyaboginArtem Zvavitch 52A3852A2042B10Brunn-Minkowski-Firey theoryShepard problemprojectionsFourier transformParseval's identity 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. Indiana University Mathematics Journal 2004 text pdf 10.1512/iumj.2004.53.2399 10.1512/iumj.2004.53.2399 en Indiana Univ. Math. J. 53 (2004) 667 - 682 state-of-the-art mathematics http://iumj.org/access/