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Quasicrystals, Almost Periodic Patterns, Mean-Periodic Functions and Irregular Sampling

Volume 13, Number 1 (2012), 7 - 45

 Quasicrystals, Almost Periodic Patterns, Mean-Periodic Functions and Irregular Sampling

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Abstract

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 areuniversal sampling sets.