Sparse Hamburger Moment Sequences and Completions in Several Variables

TL;DR

This paper characterizes sparse subsequences of Hamburger moment sequences in multiple variables and explores the problem of completing these sparse sequences, extending algebraic understanding of moment problems.

Contribution

It introduces a new characterization of sparse moment subsequences and addresses the completion problem in the multivariable Hamburger moment context.

Findings

Provided a characterization of sparse Hamburger moment subsequences.

Analyzed the problem of completing sparse moment subsequences.

Extended algebraic moment sequence theory to sparse cases.

Abstract

Putinar and Vasilescu have given an algebraic characterization of Hamburger moment sequences in several variables. In this paper we give a characterization of sparse moment subsequences of Hamburger moment sequences and consider the problem of completion of these moment subsequences.