# Multivariate moment problems : geometry and indeterminateness

Mihai Putinar; Claus Scheiderer

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2006)

- Volume: 5, Issue: 2, page 137-157
- ISSN: 0391-173X

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topPutinar, Mihai, and Scheiderer, Claus. "Multivariate moment problems : geometry and indeterminateness." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 5.2 (2006): 137-157. <http://eudml.org/doc/240335>.

@article{Putinar2006,

abstract = {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.},

author = {Putinar, Mihai, Scheiderer, Claus},

journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},

language = {eng},

number = {2},

pages = {137-157},

publisher = {Scuola Normale Superiore, Pisa},

title = {Multivariate moment problems : geometry and indeterminateness},

url = {http://eudml.org/doc/240335},

volume = {5},

year = {2006},

}

TY - JOUR

AU - Putinar, Mihai

AU - Scheiderer, Claus

TI - Multivariate moment problems : geometry and indeterminateness

JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

PY - 2006

PB - Scuola Normale Superiore, Pisa

VL - 5

IS - 2

SP - 137

EP - 157

AB - 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.

LA - eng

UR - http://eudml.org/doc/240335

ER -

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