Independent marginals of operator-semistable and operator-stable probability measures

We investigate independent marginals of full operator-semistable and operator-stable probability measures on finite-dimensional vector spaces. In particular, it is shown that for purely Poissonian operator-semistable and operator-stable distributions their independent marginals have decomposability properties of the same kind. Operator-semistability and operator-stability of independent marginals of Gaussian measures are studied in detail, and a description of independent marginals of an arbitrary operator-semistable or operator-stable distribution is obtained.