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Moment problem in infinitely many variables

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2016

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Ghasemi, Mehdi
Marshall, Murray

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https://doi.org/10.1007/s11856-016-1318-5
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Israel Journal of Mathematics. 2016, 212(2), pp. 989-1012. ISSN 0021-2172. eISSN 1565-8511. Available under: doi: 10.1007/s11856-016-1318-5

Zusammenfassung

The multivariate moment problem is investigated in the general context of the polynomial algebra R[x i | i ∈ Ω] in an arbitrary number of variables x i , i ∈ Ω. The results obtained are sharpest when the index set Ω is countable. Extensions of Haviland’s theorem [17] and Nussbaum’s theorem [34] are proved. Lasserre’s description of the support of the measure in terms of the non-negativity of the linear functional on a quadratic module of R[x i | i ∈ Ω] in [27] is shown to remain valid in this more general situation. The main tool used in the paper is an extension of the localization method developed by the third author in [30], [32] and [33]. Various results proved in [30], [32] and [33] are shown to continue to hold in this more general setting.

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510 Mathematik

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ISO 690GHASEMI, Mehdi, Salma KUHLMANN, Murray MARSHALL, 2016. Moment problem in infinitely many variables. In: Israel Journal of Mathematics. 2016, 212(2), pp. 989-1012. ISSN 0021-2172. eISSN 1565-8511. Available under: doi: 10.1007/s11856-016-1318-5
BibTex
@article{Ghasemi2016-05-26Momen-34810,
  year={2016},
  doi={10.1007/s11856-016-1318-5},
  title={Moment problem in infinitely many variables},
  number={2},
  volume={212},
  issn={0021-2172},
  journal={Israel Journal of Mathematics},
  pages={989--1012},
  author={Ghasemi, Mehdi and Kuhlmann, Salma and Marshall, Murray}
}
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