no. 7-8
Harmonic analysis
Universal sampling, quasicrystals and bounded remainder sets
[Échantillonnage universel, quasicristaux et ensembles à restes bornés]

Présenté par : Yves Meyer

Grepstad, Sigrid1 ; Lev, Nir2
1 Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
2 Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 633-638.

Nous examinons le résultat, dû à Matei et à Meyer, selon lequel les quasicristaux simples sont des ensembles d'échantillonnage universel, dans le cas critique où la densité de l'ensemble d'échantillonnage est égale à la mesure du spectre. Nous montrons que, dans ce cas, une condition arithmétique sur le quasicristal détermine s'il s'agit d'un ensemble universel d'échantillonnage « stable et non redondant ».

We examine the result due to Matei and Meyer that simple quasicrystals are universal sampling sets, in the critical case when the density of the sampling set is equal to the measure of the spectrum. We show that in this case, an arithmetical condition on the quasicrystal determines whether it is a universal set of “stable and non-redundant” sampling.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.05.006
Grepstad, Sigrid 1 ; Lev, Nir 2

1 Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway
2 Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel 
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Grepstad, Sigrid; Lev, Nir. Universal sampling, quasicrystals and bounded remainder sets. Comptes Rendus. Mathématique, Tome 352 (2014) no. 7-8, pp. 633-638. doi : 10.1016/j.crma.2014.05.006. http://www.numdam.org/articles/10.1016/j.crma.2014.05.006/

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☆ Research partially supported by the Israel Science Foundation Grant No. 225/13.