The Resolvent Matrix of the Truncated Hausdorff Matrix Moment Problem via New Dyukarev-Stieltjes Parameters and Extremal Solutions via Continued Fractions

TL;DR

This paper introduces a new multiplicative decomposition of the resolvent matrix for the truncated Hausdorff matrix moment problem, utilizing novel Dyukarev-Stieltjes parameters and continued fractions to characterize extremal solutions.

Contribution

It presents a new approach to decompose the resolvent matrix using Dyukarev-Stieltjes parameters and links these to orthogonal matrix polynomials and extremal solutions via continued fractions.

Findings

Explicit relations between DSM parameters and orthogonal matrix polynomials

New multiplicative decomposition of the resolvent matrix

Representation of extremal solutions via matrix continued fractions

Abstract

We obtain a new multiplicative decomposition of the resolvent matrix of the truncated Hausdorff matrix moment (THMM) problem in the case of an odd and even number of moments via new Dyukarev-Stieltjes matrix (DSM) parameters. Explicit interrelations between new DSM parameters and orthogonal matrix polynomials on a finite interval $[a,b]$, as well as the Schur complements of the block Hankel matrices constructed through the moments of the THMM problem are given. Additionally, the extremal solutions of the THMM problem are represented via matrix continued fractions in terms of the DSM parameters.