Moment problems related to intrinsic characterizations of the moment functionals

TL;DR

This paper characterizes moment functionals on certain algebraic structures and sets, providing new criteria that do not require positive semidefiniteness, and proves a Positivstellensatz for a specific cone.

Contribution

It introduces novel characterizations of moment functionals on compact sets and establishes a Positivstellensatz for an archimedean cone beyond quadratic modules.

Findings

Characterization of moment functionals on product of symmetric intervals

Characterization of moment functionals on arbitrary intervals

Proved a Positivstellensatz for a non-quadratic, archimedean cone

Abstract

In this paper, we consider linear functionals defined on an unital commutative real algebra A and establish characterizations for moment functionals on compact sets of characters that depend only on the given functional. For example, we obtain a characterization of a moment functional on a product of symmetric intervals, in which we do not assume that the functional is positive semidefinite but positive on a semiring of A, and a characterization of a moment functional that is a solution to the moment problem on a product of arbitrary intervals. We also prove a Positivstellensatz for an archimedean cone, which is neither a quadratic module nor a semiring.