Entropy of spherical marginals and related inequalities
Résumé
We investigate relations between the entropy of a spherical density and those of its marginals, together with spherical convolution type inequalities. We extend results by Carlen, Lieb and Loss to more general configurations. Our argument involves a corresponding superadditivity result for Fisher information, which has a clear geometric meaning. (C) 2006 Elsevier SAS. All rights reserved.