Moment problems on compacts of characters of an unital commutative algebra

TL;DR

This paper investigates the representation of nonnegative linear functionals on unital commutative algebras, providing solutions to the moment problem on compact sets of characters without assuming semiring structures.

Contribution

It offers a new integral representation for nonnegative functionals and characterizes moment functionals on compact character sets without semiring assumptions.

Findings

Integral representation for nonnegative functionals on Archimedean cones

Solution to the moment problem on products of intervals

Conditions for a functional to be a moment functional on compact character sets

Abstract

In this note we consider linear functionals on an unital commutative R-algebra. We give an integral representation of a nonnegative functional on an Archimedean cone where we do not assume that this cone is a semiring or a quadratic module. We also give a solution of the moment problem on a product of intervals and determine conditions for a functional to be a moment functional on a compact of characters.