Maria Infusino

Quasi-analyticity and Determinacy of the Full Moment Problem from Finite to Infinite Dimensions

This paper is aimed to show the essential role played by the theory of quasi-analytic functions in the study of the determinacy of the moment problem on finite and infinite-dimensional spaces. In particular, the quasi-analytic criterion of self-adjointness of operators and their commutativity are crucial to establish whether or not a measure is uniquely determined by its moments. Our main goal is to point out that this is a common feature of the determinacy question in both the finite and the infinite-dimensional moment problem, by reviewing some of the most known determinacy results from this perspective. We also collect some properties of independent interest concerning the characterization of quasi-analytic classes associated to log-convex sequences.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

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

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, T).

MOMENT PROBLEM FOR SYMMETRIC ALGEBRAS OF LOCALLY CONVEX SPACES

It is explained how a locally convex (LC) topology

Translation invariant realizability problem on the d-dimensional lattice : an explicit construction

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UNIFORM DISTRIBUTION ON FRACTALS

τ on a real vector space V extends to a locally multiplicatively convex (LMC) topology

The full moment problem on subsets of probabilities and point configurations

\overline{\tau }