Multivariable approximate Carleman-type theorems for complex measures

Isabelle Chalendar, Jonathan R. Partington
2007 Annals of Probability  
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 ${\mathbb{C}}_+^n$.
doi:10.1214/009117906000000377 fatcat:j7wm75te6feybfsifq4pgzaase