The Annals of Probability

Multivariable approximate Carleman-type theorems for complex measures

Isabelle Chalendar and Jonathan R. Partington

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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.

Article information

Source
Ann. Probab., Volume 35, Number 1 (2007), 384-396.

Dates
First available in Project Euclid: 19 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1174324134

Digital Object Identifier
doi:10.1214/009117906000000377

Mathematical Reviews number (MathSciNet)
MR2303955

Zentralblatt MATH identifier
1120.26027

Subjects
Primary: 26E10: $C^\infty$-functions, quasi-analytic functions [See also 58C25] 44A60: Moment problems
Secondary: 32A22: Nevanlinna theory (local); growth estimates; other inequalities {For geometric theory, see 32H25, 32H30} 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords
Moments of measures on ℝn functions of exponential type Denjoy–Carleman maximum principle Phragmen–Lindelof theorems

Citation

Chalendar, Isabelle; Partington, Jonathan R. Multivariable approximate Carleman-type theorems for complex measures. Ann. Probab. 35 (2007), no. 1, 384--396. doi:10.1214/009117906000000377. https://projecteuclid.org/euclid.aop/1174324134


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