The Moment Problem for Continuous Positive Semidefinite Linear Functionals


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GHASEMI, Mehdi, Salma KUHLMANN, Ebrahim SAMEI, 2012. The Moment Problem for Continuous Positive Semidefinite Linear Functionals. In: Archiv der Mathematik. 100(1), pp. 43-53. ISSN 0003-889X. eISSN 1420-8938

@article{Ghasemi2012Momen-21246, title={The Moment Problem for Continuous Positive Semidefinite Linear Functionals}, year={2012}, doi={10.1007/s00013-012-0460-5}, number={1}, volume={100}, issn={0003-889X}, journal={Archiv der Mathematik}, pages={43--53}, author={Ghasemi, Mehdi and Kuhlmann, Salma and Samei, Ebrahim} }

<rdf:RDF xmlns:rdf="" xmlns:bibo="" xmlns:dc="" xmlns:dcterms="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:creator>Kuhlmann, Salma</dc:creator> <dc:creator>Ghasemi, Mehdi</dc:creator> <dc:contributor>Kuhlmann, Salma</dc:contributor> <dcterms:issued>2012</dcterms:issued> <dc:contributor>Samei, Ebrahim</dc:contributor> <dc:contributor>Ghasemi, Mehdi</dc:contributor> <dc:date rdf:datatype="">2013-01-25T10:37:24Z</dc:date> <dc:language>eng</dc:language> <dcterms:available rdf:datatype="">2013-01-25T10:37:24Z</dcterms:available> <dcterms:abstract xml:lang="eng">Let τ be a locally convex topology on the countable dimensional polynomial ${\mathbb{R}}$ -algebra ${\mathbb{R} [\underline{X}] := \mathbb{R} [X_1, \ldots, X_{n}]}$ . Let K be a closed subset of ${\mathbb{R} ^{n}}$ , and let ${M := M_{\{g_1, \ldots, g_s\}}}$ be a finitely generated quadratic module in ${\mathbb{R} [\underline{X}]}$ . We investigate the following question: When is the cone Psd(K) (of polynomials nonnegative on K) included in the closure of M? We give an interpretation of this inclusion with respect to representing continuous linear functionals by measures. We discuss several examples; we compute the closure of ${M = \sum \mathbb{R} [\underline{X}]^{2}}$ with respect to weighted norm-p topologies. We show that this closure coincides with the cone Psd(K) where K is a certain convex compact polyhedron.</dcterms:abstract> <dcterms:title>The Moment Problem for Continuous Positive Semidefinite Linear Functionals</dcterms:title> <dcterms:rights rdf:resource=""/> <dc:creator>Samei, Ebrahim</dc:creator> <dc:rights>deposit-license</dc:rights> <dcterms:bibliographicCitation>Archiv der Mathematik ; 100 (2013), 1. - S. 43-53</dcterms:bibliographicCitation> <bibo:uri rdf:resource=""/> </rdf:Description> </rdf:RDF>

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