The realizability problem as a special case of the infinite-dimensional truncated moment problem
Abstract
The realizability problem is a well-known problem in the analysis of complex systems, which can be modeled as an infinite-dimensional moment problem. More precisely, as a truncated moment problem where is the space of all possible configurations of the components of the considered system. The power of this reformulation has been already exploited in \cite{KuLeSp11}, where necessary and sufficient conditions of Haviland type have been obtained for several instances of the realizability problem. In this article we exploit this same reformulation to apply to the realizability problem the recent advances obtained in \cite{CGIK2022} for the truncated moment problem for linear functionals on general unital commutative algebras. This provides alternative proofs and sometimes extensions of several results in \cite{KuLeSp11}, allowing to finally embed them in the unified framework for the infinite-dimensional truncated moment problem presented in \cite{CGIK2022}.
Keywords
Cite
@article{arxiv.2305.10343,
title = {The realizability problem as a special case of the infinite-dimensional truncated moment problem},
author = {Raúl E. Curto and Maria Infusino},
journal= {arXiv preprint arXiv:2305.10343},
year = {2023}
}