Multivariable approximate Carleman-type theorems for complex measures

Abstract

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.