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.
@article{ASNSP_2006_5_5_2_137_0, author = {Putinar, Mihai and Scheiderer, Claus}, title = {Multivariate moment problems : geometry and indeterminateness}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {137--157}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 5}, number = {2}, year = {2006}, mrnumber = {2244695}, zbl = {1170.44302}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2006_5_5_2_137_0/} }
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 SP - 137 EP - 157 VL - 5 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2006_5_5_2_137_0/ LA - en ID - ASNSP_2006_5_5_2_137_0 ER -
%0 Journal Article %A Putinar, Mihai %A Scheiderer, Claus %T Multivariate moment problems : geometry and indeterminateness %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2006 %P 137-157 %V 5 %N 2 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2006_5_5_2_137_0/ %G en %F ASNSP_2006_5_5_2_137_0
Putinar, Mihai; Scheiderer, Claus. Multivariate moment problems : geometry and indeterminateness. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 2, pp. 137-157. http://archive.numdam.org/item/ASNSP_2006_5_5_2_137_0/
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