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# Moment problem in infinitely many variables

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Type of Publication: | Journal article |

Publication status: | Published |

Author: | Ghasemi, Mehdi; Kuhlmann, Salma; Marshall, Murray |

Year of publication: | 2016 |

Published in: | Israel Journal of Mathematics ; 212 (2016), 2. - pp. 989-1012. - ISSN 0021-2172. - eISSN 1565-8511 |

DOI (citable link): | https://dx.doi.org/10.1007/s11856-016-1318-5 |

Summary: |
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. |

Subject (DDC): | 510 Mathematics |

Bibliography of Konstanz: | Yes |

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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. Available under: doi: 10.1007/s11856-016-1318-5

@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} }