Positive definite Hankel matrix completions and Hamburger moment completions

TL;DR

This paper characterizes which patterns of missing entries in partial positive sequences can be completed to form a full Hamburger moment sequence, providing solutions to moment problems with incomplete data.

Contribution

It introduces a characterization of positive definite completable patterns for Hamburger moment problems, advancing understanding of partial sequence completion.

Findings

Identifies patterns guaranteeing Hamburger moment completion

Provides examples of patterns not completable

Advances theoretical understanding of moment sequence completion

Abstract

In this paper we give solutions to Hamburger moment problems with missing entries. The problem of completing partial positive sequences is considered. The main result is a characterization of positive definite completable patterns, namely patterns that guarantee the existence of Hamburger moment completion of a partial positive definite sequence. Moreover, several patterns which are not positive definite completable are given.