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

Chalendar, Isabelle; Partington, Jonathan R.

Ann. Probab. 35, No. 1, 384-396 (2007).

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 \({\mathbb R}^n_{+}\).

Reviewer: Sergei V. Rogosin (Minsk)

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

Keywords:

complex measure on \({\mathbb R}^n\); moments of measures; Denjoy-Carleman maximum principle; Phragmén-Lindelöf theorems

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