Suppose that is a finitely generated commutative unital real algebra and K is a closed subset of the set  of characters of . We study the following problem: When is { each} linear functional L: → an integral with respect to some signed Radon measure on ̂ supported by the set K? A complete characterization of the sets K and algebras by necessary and sufficient conditions is given. The result is applied to the polynomial algebra [x₁,,xd] and subsets K of ᵈ.
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Konrad Schmüdgen (2024) studied this question.
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