Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions
Abstract
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.
Keywords
Cite
@article{arxiv.1405.3573,
title = {Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions},
author = {Maria Infusino},
journal= {arXiv preprint arXiv:1405.3573},
year = {2016}
}
Comments
28 pages, Stochastic and Infinite Dimensional Analysis, Chapter 9, Trends in Mathematics, Birkh\"auser Basel, 2016