Positive Riesz distributions on homogeneous cones

Abstract

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