Existence of quasicrystals and universal stable sampling and interpolation in LCA groups

AGORA, ELONA; ANTEZANA, JORGE; CABRELLI, CARLOS; MATEI, BASARAB

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

Año: 2019 vol. 372 p. 4647 - 4674

0002-9947

We characterize all the locally compact abelian (LCA) groups that contain quasicrystals (a class of model sets). Moreover, we describe all possible quasicrystals in the group constructing an appropriate lattice associated with the cut and project scheme that produces it. On the other hand, if an LCA group G admits a simple quasicrystal, we prove that recent results of Meyer and Matei for the case of the Euclidean space Rn can be extended to G. More precisely, we prove that simple quasicrystals are universal sets of stable sampling and universal sets of stable interpolation in generalized Paley-Wiener spaces.