The Resolvent Matrix for the Hausdorff Matrix Moment Problem Expressed in Terms of Orthogonal Matrix Polynomials

Abstract

This paper continues the former joint investigations of the author with Yu. M. Dyukarev, B. Fritzsche and B. Kirstein on the matrix version of the truncated Hausdorff power moment problem on an intervall \([a,b]\) for a given sequence \((s_j)_{j=0}^{2n}\) of complex \(q\times q\) matrices. The main aim is to obtain more information on the resolvent matrix. We show that the canonical \({q\times q}\) blocks of the resolvent matrix are \(q\times q\) matrix polynomials having special orthogonality properties with respect to the original data \((s_j)_{j=0}^{2n}\).