Multivariate moment problems : geometry and indeterminateness

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2006
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Putinar, Mihai
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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 is virtually compact; a generalization to higher dimensions is also given. Among the one-dimensional sets which are not virtually compact, we show that at least a large subclass supports indeterminate moment sequences. Moreover, we prove that the determinateness of a moment sequence is implied by the same condition (in general easier to verify) of the push-forward sequence via finite morphisms.

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510 Mathematik
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ISO 690PUTINAR, Mihai, Claus SCHEIDERER, 2006. Multivariate moment problems : geometry and indeterminateness. In: Annali della Scuola Normale Superiore di Pisa – Classe di Scienze. 2006, 5(2), pp. 137-157. ISSN 0391-173X. eISSN 2036-2145. Available under: doi: 10.2422/2036-2145.2006.2.01
BibTex
@article{Putinar2006Multi-23296,
  year={2006},
  doi={10.2422/2036-2145.2006.2.01},
  title={Multivariate moment problems : geometry and indeterminateness},
  number={2},
  volume={5},
  issn={0391-173X},
  journal={Annali della Scuola Normale Superiore di Pisa – Classe di Scienze},
  pages={137--157},
  author={Putinar, Mihai and Scheiderer, Claus}
}
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