A moment problem for pseudo-positive definite functionals

TL;DR

This paper introduces a moment problem for pseudo-positive measures, establishing existence and uniqueness results for representing measures of pseudo-positive definite functionals, and discusses the truncated moment problem.

Contribution

It presents a new moment problem framework for pseudo-positive measures, proving existence and determinacy conditions for representing measures.

Findings

Existence of pseudo-positive measures for pseudo-positive definite functionals.

Characterization of determinacy in pseudo-positive measure representations.

Discussion of the truncated moment problem for pseudo-positive measures.

Abstract

A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to some reasonable restrictions) there exists a representing pseudo-positive measure. The second main result is a characterization of determinacy in the class of equivalent pseudo-positive representation measures. Finally the corresponding truncated moment problem is discussed.