Multivariable approximate Carleman-type theorems for complex measures

Isabelle Chalendar; Jonathan R. Partington

doi:10.1214/009117906000000377

Multivariable approximate Carleman-type theorems for complex measures

Probability 2007-05-23 v1

Authors: Isabelle Chalendar , Jonathan R. Partington

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Abstract

We prove a multivariable approximate Carleman theorem on the determination of complex measures on ${\mathbb{R}}^n$ and ${\mathbb{R}}^n_+$ 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 Phragm\'{e}n--Lindel\"{o}f-type theorem for analytic functions on ${\mathbb{C}}_+^n$ .

Keywords

function spaces and inequalities measure theory general mathematical theorems and proofs

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@article{arxiv.math/0703809,
  title  = {Multivariable approximate Carleman-type theorems for complex measures},
  author = {Isabelle Chalendar and Jonathan R. Partington},
  journal= {arXiv preprint arXiv:math/0703809},
  year   = {2007}
}

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Published at http://dx.doi.org/10.1214/009117906000000377 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Multivariable approximate Carleman-type theorems for complex measures

Abstract

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