Positive Riesz distributions on homogeneous cones

Abstract

Riesz distributions are relatively invariant distributions supported by the closure overline{Ω} of a homogeneous cone Ω. In this paper, we clarify the positivity condition of Riesz distributions by relating it to the orbit structure of overline{Ω}. Moreover each of the positive Riesz distributions is described explicitly as a measure on an orbit in overline{Ω}.