Revista Matemática Iberoamericana

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Volume 32, Issue 4, 2016, pp. 1341–1352
DOI: 10.4171/RMI/920

Published online: 2016-12-16

Quasicrystals with discrete support and spectrum

Nir Lev[1] and Alexander Olevskii[2]

(1) Bar-Ilan University, Ramat Gan, Israel
(2) Tel Aviv University, Israel

We proved recently that a measure on $\mathbb R$, whose support and spectrum are both uniformly discrete sets, must have a periodic structure. Here we show that this is not the case if the support and the spectrum are just discrete closed sets.

Keywords: Quasicrystals, Poisson summation formula, cut-and-project, model set

Lev Nir, Olevskii Alexander: Quasicrystals with discrete support and spectrum. Rev. Mat. Iberoam. 32 (2016), 1341-1352. doi: 10.4171/RMI/920