Multivariable approximate Carleman-type theorems for complex measures

Abstract

We prove a multivariable approximate Carleman theorem on the determination of complex measures on ${\mathbb{R}}^n$ and ${\mathbb{R}}^n_+$ by their moments. This is achieved by means of a multivariable Denjoy--Carleman maximum principle for quasi-analytic functions of several variables. As an application, we obtain a discrete Phragm\'{e}n--Lindel\"{o}f-type theorem for analytic functions on ${\mathbb{C}}_+^n$.Comment: Published at http://dx.doi.org/10.1214/009117906000000377 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org