Riesz distributions are relatively invariant distributions supported by the closure of a homogeneous cone . In this paper, we clarify the positivity condition of Riesz distributions by relating it to the orbit structure of . Moreover each of the positive Riesz distributions is described explicitly as a measure on an orbit in .
Hideyuki ISHI. "Positive Riesz distributions on homogeneous cones." J. Math. Soc. Japan 52 (1) 161 - 186, January, 2000. https://doi.org/10.2969/jmsj/05210161