## Multivariable approximate Carleman-type theorems for complex measures.(English)Zbl 1120.26027

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 $${\mathbb R}^n_{+}$$.

### MSC:

 26E10 $$C^\infty$$-functions, quasi-analytic functions 32A22 Nevanlinna theory; growth estimates; other inequalities of several complex variables 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 44A60 Moment problems
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### References:

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