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

Jean Pierre Kahane; Yitzhak Katznelson

doi:10.1016/j.crma.2007.06.001

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

Translated title of the contribution: Random sequences of integers, Sidon sets, density in the Bohr group, and sets of analyticity

Jean Pierre Kahane^*
, Yitzhak Katznelson

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We study properties of a sequence Λ obtained by a random selection of integers n, where n ∈ Λ with probability π{variant}_n, independently of the other choices. We distinguish two cases: if lim sup_{n → ∞} n π{variant}_n < ∞, Λ is a.s. a Sidon set, non-dense in the Bohr group; if lim_{n → ∞} n π{variant}_n = ∞, then Λ is a.s. a set of analyticity and is dense in the Bohr group. To cite this article: J.-P. Kahane, Y. Katznelson, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

Translated title of the contribution	Random sequences of integers, Sidon sets, density in the Bohr group, and sets of analyticity
Original language	French
Pages (from-to)	21-24
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	345
Issue number	1
DOIs	https://doi.org/10.1016/j.crma.2007.06.001
State	Published - 1 Jul 2007
Externally published	Yes

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title = "Entiers al{\'e}atoires, ensembles de Sidon, densit{\'e} dans le groupe de Bohr et ensembles d'analyticit{\'e}",

abstract = "We study properties of a sequence Λ obtained by a random selection of integers n, where n ∈ Λ with probability π\{variant\}n, independently of the other choices. We distinguish two cases: if lim supn → ∞ n π\{variant\}n < ∞, Λ is a.s. a Sidon set, non-dense in the Bohr group; if limn → ∞ n π\{variant\}n = ∞, then Λ is a.s. a set of analyticity and is dense in the Bohr group. To cite this article: J.-P. Kahane, Y. Katznelson, C. R. Acad. Sci. Paris, Ser. I 345 (2007).",

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N2 - We study properties of a sequence Λ obtained by a random selection of integers n, where n ∈ Λ with probability π{variant}n, independently of the other choices. We distinguish two cases: if lim supn → ∞ n π{variant}n < ∞, Λ is a.s. a Sidon set, non-dense in the Bohr group; if limn → ∞ n π{variant}n = ∞, then Λ is a.s. a set of analyticity and is dense in the Bohr group. To cite this article: J.-P. Kahane, Y. Katznelson, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

AB - We study properties of a sequence Λ obtained by a random selection of integers n, where n ∈ Λ with probability π{variant}n, independently of the other choices. We distinguish two cases: if lim supn → ∞ n π{variant}n < ∞, Λ is a.s. a Sidon set, non-dense in the Bohr group; if limn → ∞ n π{variant}n = ∞, then Λ is a.s. a set of analyticity and is dense in the Bohr group. To cite this article: J.-P. Kahane, Y. Katznelson, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

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

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