Moment problem in infinitely many variables

Publikationstyp: Zeitschriftenartikel
Publikationsstatus: Published
Autor/innen: Ghasemi, Mehdi; Kuhlmann, Salma; Marshall, Murray
Erscheinungsjahr: 2016
Erschienen in: Israel Journal of Mathematics ; 212 (2016), 2. - S. 989-1012. - ISSN 0021-2172. - eISSN 1565-8511
DOI (zitierfähiger Link): https://dx.doi.org/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.
Fachgebiet (DDC): 510 Mathematik
Universitätsbibliographie: Ja

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GHASEMI, Mehdi, Salma KUHLMANN, Murray MARSHALL, 2016. Moment problem in infinitely many variables. In: Israel Journal of Mathematics. 212(2), pp. 989-1012. ISSN 0021-2172. eISSN 1565-8511

@article{Ghasemi2016-05-26Momen-34810, title={Moment problem in infinitely many variables}, year={2016}, doi={10.1007/s11856-016-1318-5}, number={2}, volume={212}, issn={0021-2172}, journal={Israel Journal of Mathematics}, pages={989--1012}, author={Ghasemi, Mehdi and Kuhlmann, Salma and Marshall, Murray} }

Marshall, Murray Kuhlmann, Salma Moment problem in infinitely many variables Marshall, Murray Ghasemi, Mehdi 2016-07-15T12:45:06Z The multivariate moment problem is investigated in the general context of the polynomial algebra R[x<sub> i</sub> | i ∈ Ω] in an arbitrary number of variables x<sub> i</sub> , 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<sub> i</sub> | 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. 2016-05-26 2016-07-15T12:45:06Z eng Kuhlmann, Salma Ghasemi, Mehdi

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