Moment problem in infinitely many variables

Ghasemi, Mehdi; Kuhlmann, Salma; Marshall, Murray

Moment problem in infinitely many variables

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Date

2014

Authors

Ghasemi, Mehdi

Kuhlmann, Salma

Marshall, Murray

ArXiv-ID

1409.5777

Collections

Mathematik und Statistik

Publication type

Preprint

Abstract

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.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

GHASEMI, 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@unpublished{Ghasemi2014Momen-30958,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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