On the determinacy of the moment problem for symmetric algebras of a locally convex space

Maria Infusino, Salma Kuhlmann, Murray Marshall

Published 2016-03-24Version 1

This note aims to show a uniqueness property for the solution (whenever exists) to the moment problem for the symmetric algebra $S(V)$ of a locally convex space $V$. Given the existence of a measure $\mu$ representing a linear functional $L: S(V)\to\mathbb{R}$, we deduce a sufficient determinacy condition on $L$ provided that the support of $\mu$ is contained in a countable union of some topological duals of $V$. We will compare this result with some already known in literature for such a general form of the moment problem and further discuss how some prior knowledge on the support of the representing measure influences its determinacy.