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Multivariate moment problems : geometry and indeterminateness

Mihai PutinarClaus Scheiderer — 2006

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The most accurate determinateness criteria for the multivariate moment problem require the density of polynomials in a weighted Lebesgue space of a generic representing measure. We propose a relaxation of such a criterion to the approximation of a single function, and based on this condition we analyze the impact of the geometry of the support on the uniqueness of the representing measure. In particular we show that a multivariate moment sequence is determinate if its support has dimension one and...

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