On the multidimensional K-moment problem

TL;DR

This paper establishes a new solvability criterion for the multidimensional Stieltjes moment problem, extending classical results to multivariate and semi-algebraic unbounded sets, with implications for moment problem theory.

Contribution

It introduces a novel multivariate Stieltjes condition that guarantees solvability of the moment problem on $\mathbb{R}^d$ and unbounded semi-algebraic subsets.

Findings

Proves a solvability theorem based on a multivariate Stieltjes condition.

Derives a new solvability criterion for the moment problem on unbounded semi-algebraic sets.

Extends classical moment problem results to higher dimensions and more general sets.

Abstract

We prove a solvability theorem for the Stieltjes moment problem on $R^d$ which is based on the multivariate Stieltjes condition $\sum_{n=1}^\infty L(x_j^n)^{-1/(2n)}=+\infty$, $j=1,\dots,d.$ This result is applied to derive a new solvability theorem for the moment problem on unbounded semi-algebraic subsets of $R^d$.