On the Moment Functionals with Signed Representing Measures

2024/05/14 by Schmüdgen, Konrad · 1 citation
#44 A 60 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2405.08899

Abstract

Suppose that \sA is a finitely generated commutative unital real algebra and K is a closed subset of the set A of characters of \sA. We study the following problem: When is \it each linear functional L:\sA → \dR an integral with respect to some signed Radon measure on \sA supported by the set K? A complete characterization of the sets K and algebras \sA by necessary and sufficient conditions is given. The result is applied to the polynomial algebra \dR[x₁,…,x_d] and subsets K of \dR^d.

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