Abstract
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.
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Murray Marshall passed away on May 1, 2015. We lost a wonderful collaborator and a dear friend. We miss him sorely.
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Ghasemi, M., Kuhlmann, S. & Marshall, M. Moment problem in infinitely many variables. Isr. J. Math. 212, 1012 (2016). https://doi.org/10.1007/s11856-016-1318-5
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DOI: https://doi.org/10.1007/s11856-016-1318-5