The Nevanlinna-type formula for the truncated matrix trigonometric moment problem

TL;DR

This paper extends the theory of the truncated matrix trigonometric moment problem by deriving a Nevanlinna-type formula applicable in general cases, explicitly expressing transformation coefficients and providing conditions for determinacy.

Contribution

It introduces a general Nevanlinna-type formula for the problem, with explicit coefficients and solvability conditions, advancing the understanding of solution structures.

Findings

Derived a Nevanlinna-type formula for the moment problem

Expressed transformation coefficients explicitly in terms of moments

Provided conditions for the problem's determinacy

Abstract

This paper is a continuation of our previous investigation on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, 63, no.6, 786-797. In the present paper we obtain a Nevanlinna-type formula for this moment problem in a general case. We only assume that we have more than one moment, the moment problem is solvable and the problem has more than one solution. The coefficients of the corresponding matrix linear fractional transformation are explicitly expressed by the prescribed moments. Easy conditions for the determinacy of the moment problem are given.