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Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions

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2016

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https://doi.org/10.1007/978-3-319-07245-6_9
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BERNIDO, Christopher, ed. and others. Stochastic and Infinite Dimensional Analysis. Basel: Birkhäuser, 2016, pp. 161-194. Trends in Mathematics. ISSN 2297-0215. ISBN 978-3-319-07244-9. Available under: doi: 10.1007/978-3-319-07245-6_9

Zusammenfassung

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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Fachgebiet (DDC)
510 Mathematik

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Moment problem; determinacy; quasi-analytic class; infinite dimensional moment problem; realizability; nuclear space; convex regularization; log-convexity

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Stochastic and Infinite Dimensional Analysis, 24. Juni 2013 - 28. Juni 2013, Bielefeld
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ISO 690INFUSINO, Maria, 2016. Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions. Stochastic and Infinite Dimensional Analysis. Bielefeld, 24. Juni 2013 - 28. Juni 2013. In: BERNIDO, Christopher, ed. and others. Stochastic and Infinite Dimensional Analysis. Basel: Birkhäuser, 2016, pp. 161-194. Trends in Mathematics. ISSN 2297-0215. ISBN 978-3-319-07244-9. Available under: doi: 10.1007/978-3-319-07245-6_9
BibTex
@inproceedings{Infusino2016Quasi-34833,
  year={2016},
  doi={10.1007/978-3-319-07245-6_9},
  title={Quasi-analyticity and determinacy of the full moment problem from finite to infinite dimensions},
  isbn={978-3-319-07244-9},
  issn={2297-0215},
  publisher={Birkhäuser},
  address={Basel},
  series={Trends in Mathematics},
  booktitle={Stochastic and Infinite Dimensional Analysis},
  pages={161--194},
  editor={Bernido, Christopher},
  author={Infusino, Maria}
}
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