The Nevanlinna-type formula for the matrix Hamburger moment problem in a general case

TL;DR

This paper derives a Nevanlinna-type formula for the matrix Hamburger moment problem, providing explicit expressions for the solutions and conditions for their uniqueness in a general setting.

Contribution

It introduces a general Nevanlinna-type formula for the matrix Hamburger moment problem, expressing solutions via linear fractional transformations based on given moments.

Findings

Explicit formula for solutions in terms of moments

Conditions for problem determinacy

Characterization of multiple solutions

Abstract

In this paper we obtain a Nevanlinna-type formula for the matrix Hamburger moment problem in a general case. We only assume that the problem is solvable and has more that one solution. We express the matrix coefficients of the corresponding linear fractional transformation in terms of the prescribed moments. Necessary and sufficient conditions for the determinacy of the moment problem are given.