Dyukarev–Stieltjes parameters of the truncated Hausdorff matrix moment problem

Abstract

We obtain a new multiplicative decomposition of the resolvent matrix of the non-degenerate truncated Hausdorff matrix moment (THMM) problem in the case of odd and even number of moments with the help of Dyukarev–Stieltjes matrix parameters (DSMP). Our result generalizes the Dyukarev representation of the resolvent matrix of the truncated Stieltjes matrix moment problem published in (Math Notes 75(1–2):66–82, 2004). In the scalar case, these parameters appear in the celebrated Stieltjes’s (1894) work Recherches sur les fractions continues and are used to establish the determinateness of the moment problem. We also obtain explicit relations between four families of orthogonal matrix polynomials on [a, b] together with their matrix polynomials of the second kind and the DSMP of the THMM problem. Additionally, we derive new representations of the Christoffel–Darboux kernel.