Explicit relation between two resolvent matrices of the truncated Hausdorff matrix moment problem

TL;DR

This paper establishes an explicit connection between two resolvent matrices associated with the truncated Hausdorff matrix moment problem, utilizing orthogonal matrix polynomials and their second kind polynomials.

Contribution

It introduces a novel explicit relation between resolvent matrices for THMM, involving four families of orthogonal matrix polynomials on a finite interval.

Findings

Derived explicit relations between resolvent matrices for even and odd moments

Connected resolvent matrices with orthogonal matrix polynomials and second kind polynomials

Enhanced understanding of the structure of solutions to the truncated Hausdorff matrix moment problem

Abstract

We consider the explicit relation between two resolvent matrices related to the truncated Hausdorff matrix moment problem (THMM) in the case of an even and odd number of moments. This relation is described with the help of four families of orthogonal matrix polynomials on the finite interval $[a,b]$ and their associated second kind polynomials.