Projective Limit Techniques for the Infinite Dimensional Moment Problem

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INFUSINO, Maria, Salma KUHLMANN, Tobias KUNA, Patrick MICHALSKI, 2022. Projective Limit Techniques for the Infinite Dimensional Moment Problem. In: Integral Equations and Operator Theory. Springer. 94(2), 12. ISSN 0378-620X. eISSN 1420-8989. Available under: doi: 10.1007/s00020-022-02692-6

@article{Infusino2022-06Proje-57268, title={Projective Limit Techniques for the Infinite Dimensional Moment Problem}, year={2022}, doi={10.1007/s00020-022-02692-6}, number={2}, volume={94}, issn={0378-620X}, journal={Integral Equations and Operator Theory}, author={Infusino, Maria and Kuhlmann, Salma and Kuna, Tobias and Michalski, Patrick}, note={Article Number: 12} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:creator>Kuna, Tobias</dc:creator> <dc:creator>Infusino, Maria</dc:creator> <dcterms:hasPart rdf:resource=""/> <dc:contributor>Michalski, Patrick</dc:contributor> <dc:creator>Michalski, Patrick</dc:creator> <dc:language>eng</dc:language> <dcterms:rights rdf:resource=""/> <dc:contributor>Infusino, Maria</dc:contributor> <dcterms:abstract xml:lang="eng">We deal with the following general version of the classical moment problem: when can a linear functional on a unital commutative real algebra A be represented as an integral with respect to a Radon measure on the character space X(A) of A equipped with the Borel σ-algebra generated by the weak topology? We approach this problem by constructing X(A) as a projective limit of the character spaces of all finitely generated unital subalgebras of A. Using some fundamental results for measures on projective limits of measurable spaces, we determine a criterion for the existence of an integral representation of a linear functional on A with respect to a measure on the cylinder σ-algebra on X(A) (resp. a Radon measure on the Borel σ-algebra on X(A)) provided that for any finitely generated unital subalgebra of A the corresponding moment problem is solvable. We also investigate how to localize the support of representing measures for linear functionals on A. These results allow us to establish infinite dimensional analogues of the classical Riesz-Haviland and Nussbaum theorems as well as a representation theorem for linear functionals non-negative on a “partially Archimedean” quadratic module of A. Our results in particular apply to the case when A is the algebra of polynomials in infinitely many variables or the symmetric tensor algebra of a real infinite dimensional vector space, providing a unified setting which enables comparisons between some recent results for these instances of the moment problem.</dcterms:abstract> <dc:creator>Kuhlmann, Salma</dc:creator> <dspace:hasBitstream rdf:resource=""/> <dc:rights>Attribution 4.0 International</dc:rights> <bibo:uri rdf:resource=""/> <dcterms:available rdf:datatype="">2022-04-13T14:15:56Z</dcterms:available> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:contributor>Kuna, Tobias</dc:contributor> <dc:date rdf:datatype="">2022-04-13T14:15:56Z</dc:date> <dcterms:isPartOf rdf:resource=""/> <dcterms:issued>2022-06</dcterms:issued> <dspace:isPartOfCollection rdf:resource=""/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:contributor>Kuhlmann, Salma</dc:contributor> <dcterms:title>Projective Limit Techniques for the Infinite Dimensional Moment Problem</dcterms:title> </rdf:Description> </rdf:RDF>

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