Tracial moment problems on hypercubes

TL;DR

This paper introduces and solves the tracial and matrix-valued K-moment problems on hypercubes, establishing their equivalence and providing solutions using a matrix polynomial version of Haviland's theorem.

Contribution

It defines new moment problems in the matrix and tracial setting and proves their equivalence, offering solutions specifically for hypercube domains.

Findings

Established the equivalence of tracial and matrix-valued K-moment problems.

Solved the K-moment problems for the hypercube domain.

Applied a Haviland's theorem for matrix polynomials to obtain solutions.

Abstract

In this paper we introduce the "tracial $K$-moment problem" and the "sequential matrix-valued $K$-moment problem" and show the equivalence of the solvability of these problems. Using a Haviland's theorem for matrix polynomials, we solve these $K$-moment problems for the case where $K$ is the hypercube $[-1,1]^n$.