Idempotents and moment problem for discrete measure

In this paper, we investigate the full multidimensional moment problem for discrete measure using Vasilescu's idempotent approach based on Λ-multiplicative elements with respect to the associated square positive Riesz functional Λ. We give a sufficient condition for the existence of a discrete integral representation of the Riesz functional Λ, which turns out to be necessary in the bounded shift space case (in fact, it suffices to assume the density of polynomials in the corresponding L2-space). We pay special attention to Λ-multiplicative elements, providing several criteria guaranteeing that they are characteristic functions of single point sets. We also give an example showing that Λ-multiplicative elements may not be characteristic functions of single point sets. © 2021 Elsevier Inc.