# A description of all solutions of the matrix Hamburger moment problem in a general case

## TL;DR

This paper provides a comprehensive description of all solutions to the matrix Hamburger moment problem in general, utilizing generalized resolvents of symmetric operators, and addresses specific cases including truncated problems with odd and even moments.

## Contribution

It extends the understanding of the matrix Hamburger moment problem by describing all solutions in the general case and analyzing special truncated cases with new solvability conditions.

## Key findings

- All solutions of the matrix Hamburger moment problem are characterized in the general case.
- Solutions for the truncated problem with an odd number of moments are described in an 'almost nondegenerate' case.
- Conditions for solvability of the scalar truncated problem with an even number of moments are provided.

## Abstract

We describe all solutions of the matrix Hamburger moment problem in a general case (no conditions besides solvability are assumed). We use the fundamental results of A.V. Shtraus on the generalized resolvents of symmetric operators. All solutions of the truncated matrix Hamburger moment problem with an odd number of given moments are described in an "almost nondegenerate" case. Some conditions of solvability for the scalar truncated Hamburger moment problem with an even number of given moments are given.