Truncated moment problems for representing densities and the Riesz-Haviland theorem

Mathematics – Functional Analysis

Scientific paper

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Submitted to J. Operator Theory. Typos and wrong expressions corrected, reference added

Scientific paper

We prove a result of extension for linear functionals from a subspace to the whole space with the preservation of a certain strict positivity property. As a consequence we obtain a Riesz-Haviland type result characterizing the existence of the absolutely continuous representing measures in the multivariate truncated moment problems. This property turns to describe the dense interior of the convex cone of all truncated data having representing measures.

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