The aim of the presentation is to outline a proof that quasicrystals in Euclidean space are sampling sets for Paley-Wiener spaces of band-limited functions. The presented results show that Landau's necessary density conditions for sampling are also sufficient for some sets.
Reference:
Matei, B., Meyer, M. A variant of compressed sensing. Rev. Mat. Iberoam. 25, No.2, 669-692 (2009).
Matei, B., Meyer, M. Simple quasicrystals are set of stable sampling. Complex Var. Elliptic Equ. 55, No 8-10, 947-964 (2010).