Riesz potentials associated with the composite power function on the space of rectangular matrices

On the space of real rectangular matrices, Riesz potentials depending on a multidimensional complex parameter are studied. These potentials are in relationship with the composite power function of a matrix argument. For the potentials indicated, analogs of classical equalities are established. In particular, the semigroup property for the Riesz potentials with multidimensional complex parameter is proved under less restrictive limitations on the parameters of a rectangular matrix than the corresponding semigroup property for the Riesz potentials of one complex parameter.