Determinate multidimensional measures, the extended Carleman theorem and quasi-analytic weights
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Marcel de Jeu [1]
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[1] Leiden University
Leiden University
Países Bajos
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- Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 3, 2003, págs. 1205-1227
- Idioma: inglés
- DOI: 10.1214/aop/1055425776
- Texto completo no disponible (Saber más ...)
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Resumen
We prove in a direct fashion that a multidimensional probability measure μ is determinate if the higher-dimensional analogue of Carleman's condition is satisfied. In that case, the polynomials, as well as certain proper subspaces of the trigonometric functions, are dense in all associated Lp-spaces for 1≤p<∞. In particular these three statements hold if the reciprocal of a quasi-analytic weight has finite integral under μ. We give practical examples of such weights, based on their classification.
As in the one-dimensional case, the results on determinacy of measures supported on \Rn lead to sufficient conditions for determinacy of measures supported in a positive convex cone, that is, the higher-dimensional analogue of determinacy in the sense of Stieltjes.
