We prove a solvability theorem for the Stieltjes problem on \(\mathbb {R}^d\) 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 \(\mathbb {R}^d\).

中文翻译：

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Stieltjes条件和多维$$ {\ mathcal {K}} $$ K-矩问题

我们证明了基于多元Stieltjes条件\（\ sum _ {n = 1} ^ \ infty L（x_j ^ {n}）的\（\ mathbb {R} ^ d \）上的Stieltjes问题的可解性定理^ {-1 /（2n）} = + \ infty \），\（j = 1，\ dots，d。\）这个结果被用来导出关于矩的无界半代数子集的矩问题的一个新的可解性定理。\（\ mathbb {R} ^ d \）。