An Application of the Schur Complement to Truncated Matricial Power Moment Problems

TL;DR

This paper uses a Schur complement approach to provide a clearer understanding and unification of phenomena related to truncated matricial moment problems, enhancing theoretical insight into these problems.

Contribution

It introduces a novel application of the Schur complement to clarify and unify the understanding of phenomena in truncated matricial moment problems.

Findings

A new principle describing the phenomenon in truncated matricial moment problems

A unified framework for understanding these problems

Enhanced theoretical insight into the structure of solutions

Abstract

The main goal of this paper is to reconsider a phenomenon which was treated in earlier work of the authors' on several truncated matricial moment problems. Using a special kind of Schur complement we obtain a more transparent insight into the nature of this phenomenon. In particular, a concrete general principle to describe it is obtained. This unifies an important aspect connected with truncated matricial moment problems.