Dipartimento di Scienze Statistiche

  We discuss characterizations of linear functionals $L$ on an unital commutative real algebra $A$ which can be represented as integral w.r.t. a compactly supported Radon measure on the character space of $A$. We give a characterization by the following three types of conditions: bounds on the growth of $(L(a^n))_n$, non-negativity of $L$ on Archimedean quadratic models, and continuity of $L$ w.r.t. submultiplicative seminorms on $A$. We will relate each of these conditions to a different technique solving this instance of the moment problem. Surprisingly, we can also provide an exact characterization of the compact support of the representing Radon measure purely in terms of $L$. This is a joint work arXiv:2204.05630 with Maria Infusino, Salma Kuhlmann and Patrick Michalski.