Multivariable approximate Carleman-type theorems for complex measures (Q879261)

A multivariable Denjoy-Carleman maximum principle is obtained by means of a multivariable version of Bernstein's inequality for functions of exponential type. On the base of these ideas a multivariable approximate Carleman theorem on \({\mathbb R}^n\) is proved. Such theorem holds even in the case of complex measures. At the proof a variant of the Paley-Wiener-Schwartz theorem for Fourier transforms of distributions is used. An analogous result is obtained for the complex measures supported on the half-space \({\mathbb R}^n_{+}\).