On a variational approach to truncated problems of moments

TL;DR

This paper explores a variational method to determine the existence of $L^1$ solutions for truncated moments problems in multiple variables, linking solutions to the maximization of concave Lagrangian functions under support regularity conditions.

Contribution

It introduces a variational framework connecting $L^1$ solutions of truncated moments problems with the maximization of specific concave functions, under regularity assumptions.

Findings

Existence of $L^1$ solutions characterized by concave Lagrangian maximization.

Regularity assumptions on support are necessary for the characterization.

Provides a new variational approach to truncated moments problems.

Abstract

We characterize the existence of the $L^1$ solutions of the truncated moments problem in several real variables on unbounded supports by the existence of the maximum of certain concave Lagrangian functions. A natural regularity assumption on the support is required.