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

2016/11/17 by Elona Agora, Agora, E., Jorge Antezana +5
Materials Science · Mathematics · #42C15 #42C30 #43A25 #94A20 #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1611.05804

openalex publication_date 2016/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 n-dimensional Euclidean space 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.

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