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arXiv · 0705.4261

Entiers aléatoires, ensembles de Sidon, densité dans le groupe de Bohr et ensembles d'analyticité

Jean-Pierre Kahane·Yitzhak Katznelson
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Abstract

We study properties of a sequence $Λ$ obtained by a randomselection of integers $n$, where $n\inΛ$ with probability $\varpi_{n}$, independently of the other choices. We distinguish two cases : if $\limsup_{n\to\infty}n\varpi_{n}<\infty$, $Λ$ is a.s. a Sidon set, non-dense in the Bohr group ; if $\lim_{n\to\infty}n\varpi_{n}=\infty$, then $Λ$ is a.s. a set of analyticity and is dense in the Bohr group.

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Jean-Pierre Kahane, Yitzhak Katznelson. 2007-05-29. Entiers aléatoires, ensembles de Sidon, densité dans le groupe de Bohr et ensembles d'analyticité. https://arxiv.org/abs/0705.4261

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