On degenerate Hamburger moment problem and extensions of positive semidefinite Hankel block matrices

TL;DR

This paper investigates the degenerate Hamburger moment problem and positive semidefinite Hankel block matrices, providing a solution description via linear fractional transformations and exploring conditions for Hankel extensions.

Contribution

It offers a new characterization of solutions for degenerate matrix Hamburger moment problems using linear fractional transformations and analyzes conditions for Hankel matrix extensions.

Findings

Solution description via linear fractional transformation

Characterization of all solutions for degenerate problems

Conditions for positive semidefinite Hankel extensions

Abstract

In this paper we consider two related objects: singular positive semidefinite Hankel block--matrices and associated degenerate truncated matrix Hamburger moment problems. The description of all solutions of a degenerate matrix Hamburger moment problem is given in terms of a linear fractional transformation. The case of interest is the Hamburger moment problem whose Hankel block--matrix admits a positive semidefinite Hankel extension.