Moment problem in infinitely many variables

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...

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Bibliographic Details
Published in:Israel journal of mathematics 2016-05, Vol.212 (2), p.1012-1012
Main Authors: Ghasemi, Mehdi, Kuhlmann, Salma, Marshall, Murray
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-016-1318-5