On the multidimensional K-moment problem

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 $R^d$.

7 pages