Three properties of quasicrystals will be proved in this essay. Quasicrystals are almost periodic patterns (such patterns are carefully defined below). Every mean-periodic function whose spectrum is contained in a quasicrystal is almost periodic. Finally simple quasicrystals are universal sampling sets.
"Quasicrystals, Almost Periodic Patterns, Mean-periodicFunctions and Irregular Sampling." Afr. Diaspora J. Math. (N.S.) 13 (1) 1 - 45, 2012.