Truncated matricial moment problems on a finite interval: the operator approach

TL;DR

This paper characterizes all solutions to truncated matricial moment problems on finite intervals using operator theory, specifically generalized sc-resolvents of Hermitian contractions, without additional solvability conditions.

Contribution

It provides a comprehensive description of solutions to matricial moment problems employing the operator approach based on Krein and Ovcharenko's results.

Findings

Complete solution characterization for truncated matricial moment problems.

Application of generalized sc-resolvents to moment problems.

No extra conditions needed beyond solvability.

Abstract

In this paper we obtain a description of all solutions of truncated matricial moment problems on a finite interval in a general case (no conditions besides solvability are assumed). We use the basic results of M.G. Krein and I.E. Ovcharenko about generalized sc-resolvents of Hermitian contractions.