Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions
| Type of Publication: | Contribution to a conference |
| Publication status: | Published |
| Author: | Infusino, Maria |
| Year of publication: | 2016 |
| Conference: | Stochastic and Infinite Dimensional Analysis, Jun 24, 2013 - Jun 28, 2013, Bielefeld |
| Published in: | Stochastic and Infinite Dimensional Analysis / Bernido, Christopher et al. (ed.). - Basel : Birkhäuser, 2016. - (Trends in Mathematics). - pp. 161-194. - ISSN 2297-0215. - ISBN 978-3-319-07244-9 |
| DOI (citable link): | https://dx.doi.org/10.1007/978-3-319-07245-6_9 |
| Summary: |
This paper is aimed to show the essential role played by the theory of quasi-analytic functions in the study of the determinacy of the moment problem on finite and infinite-dimensional spaces. In particular, the quasi-analytic criterion of self-adjointness of operators and their commutativity are crucial to establish whether or not a measure is uniquely determined by its moments. Our main goal is to point out that this is a common feature of the determinacy question in both the finite and the infinite-dimensional moment problem, by reviewing some of the most known determinacy results from this perspective. We also collect some properties of independent interest concerning the characterization of quasi-analytic classes associated to log-convex sequences.
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| MSC Classification: | 44A60, 26E10, 47B25, 47A70, 28C05, 28C20 |
| Subject (DDC): | 510 Mathematics |
| Keywords: | Moment problem; determinacy; quasi-analytic class; infinite dimensional moment problem; realizability; nuclear space; convex regularization; log-convexity |
| Bibliography of Konstanz: | Yes |
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INFUSINO, Maria, 2016. Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions. Stochastic and Infinite Dimensional Analysis. Bielefeld, Jun 24, 2013 - Jun 28, 2013. In: BERNIDO, Christopher, ed. and others. Stochastic and Infinite Dimensional Analysis. Basel:Birkhäuser, pp. 161-194. ISSN 2297-0215. ISBN 978-3-319-07244-9. Available under: doi: 10.1007/978-3-319-07245-6_9
@inproceedings{Infusino2016Quasi-34833, title={Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions}, year={2016}, doi={10.1007/978-3-319-07245-6_9}, isbn={978-3-319-07244-9}, issn={2297-0215}, address={Basel}, publisher={Birkhäuser}, series={Trends in Mathematics}, booktitle={Stochastic and Infinite Dimensional Analysis}, pages={161--194}, editor={Bernido, Christopher}, author={Infusino, Maria} }
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