Revista Matemática Iberoamericana
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Published online: 2016-12-16
Quasicrystals with discrete support and spectrumNir Lev and Alexander Olevskii (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