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Moment problem in infinitely many variables

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2014

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Ghasemi, Mehdi
Marshall, Murray

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http://arxiv.org/abs/1409.5777

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The multivariate moment problem is investigated in the general context of the polynomial algebra R[xi∣i∈Ω] in an arbitrary number of variables xi, i∈Ω. The results obtained are sharpest when the index set Ω is countable. Extensions of Haviland's theorem [Amer. J. Math., 58 (1936) 164-168] and Nussbaum's theorem [Ark. Math., 6 (1965) 179-191] 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[xi∣i∈Ω] in [Trans. Amer. Math. Soc., 365 (2013) 2489-2504] 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.

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510 Mathematik

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ISO 690GHASEMI, Mehdi, Salma KUHLMANN, Murray MARSHALL, 2014. Moment problem in infinitely many variables
BibTex
@unpublished{Ghasemi2014Momen-30958,
  year={2014},
  title={Moment problem in infinitely many variables},
  author={Ghasemi, Mehdi and Kuhlmann, Salma and Marshall, Murray}
}
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