Supplements to operator-stable and operator-semistable laws on Euclidean spaces

Operator-stable laws and operator-semistable laws (introduced as limit distributions by M. Sharpe and R. Jajte, respectively) are characterized by decomposability properties. Disintegration of their corresponding Lévy measures requires appropriate cross sections. Furthermore in both situations the Lévy measures constitute a Bauer simplex whose extreme boundary can be explicitly given. Finally the infinitely differentiable Lebesgue density of an operator-semistable law is shown to be even analytic in some cases.