On an analytic generalization of the Busemann–Petty problem ✩

In this paper, we establish an extension of the connections between an analytic generalization of the Busemann–Petty problem and the positive definite distributions. Our results show that the structure of the positive definite distributions in Rn is closely related to the analytic generalization of the Busemann–Petty problem which was posed by Koldobsky. © 2007 Elsevier Inc. All rights reserved