On resolvent matrix, Dyukarev-Stieltjes parameters and orthogonal matrix polynomials via $[0,\infty)$-Stieltjes transformed sequences

TL;DR

This paper introduces a novel representation of the resolvent matrix for the truncated matricial Stieltjes moment problem using Schur transformed sequences and Dyukarev-Stieltjes parameters, linking orthogonal matrix polynomials to second-kind polynomials.

Contribution

It provides explicit relations between orthogonal matrix polynomials and second-kind polynomials derived from Schur transformed sequences, and identifies a non-negative Hermitian measure related to these polynomials.

Findings

New representation of the resolvent matrix for the Stieltjes moment problem

Explicit relations between orthogonal and second-kind matrix polynomials

Identification of a Hermitian measure for orthogonality

Abstract

By using Schur transformed sequences and Dyukarev-Stieltjes parameters we obtain a new representation of the resolvent matrix corresponding to the truncated matricial Stieltjes moment problem. Explicit relations between orthogonal matrix polynomials and matrix polynomials of the second kind constructed from consecutive Schur transformed sequences are obtained. Additionally, a non-negative Hermitian measure for which the matrix polynomials of the second kind are the orthogonal matrix polynomials is found.