On the truncated matricial Stieltjes moment problem $\mathsf{M}[[\alpha,\infty);(s_j)_{j=0}^m,\leq]$

TL;DR

This paper characterizes all solutions to a truncated matricial Stieltjes moment problem using Stieltjes transforms and a Schur type algorithm, covering both degenerate and non-degenerate cases.

Contribution

It provides a complete description of the solution set for the truncated matricial Stieltjes moment problem employing a Schur type algorithm.

Findings

Complete solution set characterized via Stieltjes transform.

Identification of parameter subsets corresponding to related moment problems.

Extension of previous algorithms to degenerate cases.

Abstract

This paper gives via Stieltjes transform a complete description of the solution set of a matricial truncated Stieltjes-type power moment problem in the non-degenerate and degenerate cases. The approach is based on the Schur type algorithm which was worked out in the papers [arXiv:1604.07240, arXiv:1604.07629]. Furthermore, the subset of parameters is determined which corresponds to another truncated matricial Stieltjes-type moment problem.