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Journal of Operator Theory

Volume 71, Issue 1, Winter 2014  pp. 85-93.

A Riesz-Haviland type result for truncated moment problems with solutions in $L^1$

Authors Calin-Grigore Ambrozie
Author institution: Inst. of Mathematics, AS CR, Zitna 25, 115 67 Prague 1, Czech Republic and Institute of Mathematics "Simion Stoilow", Romanian Academy, PO Box 1-764, 014700 Bucharest, Romania

Summary:  We give a version of the Riesz--Haviland theorem for truncated moments problems, characterizing the existence of the representing measures that are absolutely continuous with respect to the Lebesgue measure. The existence of such representing densities describes the dense interior of the convex cone of all data having nonnegative Borel representing measures. A natural regularity assumption on the support is required.

Keywords:  positive functional, moments problem, measure

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