Abstract
A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to some reasonable restrictions) there exists a representing pseudo-positive measure.
The second main result is a characterization of determinacy in the class of equivalent pseudo-positive representation measures. Finally the corresponding truncated moment problem is discussed.
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Both authors acknowledge the support of the Institutes Partnership Project with the Alexander von Humboldt Foundation, Bonn. The first author was partially supported by a project DO-02-275, 2008 with the National Science Foundation of Bulgaria, and a bilateral research project B-Gr17 within the Greek-Bulgarian S&T Cooperation.
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Kounchev, O., Render, H. A moment problem for pseudo-positive definite functionals. Ark Mat 48, 97–120 (2010). https://doi.org/10.1007/s11512-009-0095-3
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DOI: https://doi.org/10.1007/s11512-009-0095-3