Transformations of matricial α-Stieltjes non-negative definite sequences

Abstract

We investigate the inner structure of power moment sequences of matrix measures on the right semiaxis [α,+∞), where α is a given real number. To a given matrix sequence, we associate in a bijective way a new sequence of matrices, which we call the right α-Stieltjes parametrization. Thereby, one-to-one correspondences between power moment sequences on the right semiaxis [α,+∞) with additional properties and particular sequences of non-negative Hermitian matrices are established. We consider distinguished transformations of matrix sequences the study of which was suggested by considering some natural transformations of matrix measures on an interval. A main theme is to describe the right α-Stieltjes parametrization of the transformed sequence in terms of the right α-Stieltjes parametrization of the original sequence.