We prove a multivariable approximate Carleman theorem on the determination of complex measures on ℝn and ℝn+ 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 Phragmén–Lindelöf-type theorem for analytic functions on ℂ+n.
"Multivariable approximate Carleman-type theorems for complex measures." Ann. Probab. 35 (1) 384 - 396, January 2007. https://doi.org/10.1214/009117906000000377