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On the moment problem of closed semi-algebraic sets

Konrad Schmuedgen
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Abstract

Let $K_f$ be a closed semi-algebraic set in $\dR^d$ such that there exist bounded real polynomials $h_1,{...},h_n$ on $K_f$. It is proved that the moment problem for $K_f$ is solvable provided it is for all sets $K_f\cap C_λ$, where $C_λ=\{x:h_1(x)=λ_1,{...},h_n(x)=λ_n\}$ and $\inf\{h_j(x); x\in K_f\}\leλ_j\le\sup\{h_j(x);x\in K_f\}$. New classes of non-compact closed semi-algebraic sets $K_f$ are found for which the moment problem is solvable. To appear in Journal fuer die Reine und Angewandte Mathematik

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Konrad Schmuedgen. 2002-10-30. On the moment problem of closed semi-algebraic sets. https://arxiv.org/abs/math/0203207

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