### Browsing by Author "Klick, Anna"

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Item Diffraction of fully Euclidean model sets(2021) Klick, Anna; Strungaru, NicolaeWe provide a elementary proof, using only the Poisson summation formula and theory of tempered distributions, of the well-known fact that fully Euclidean regular model sets produce a pure point diffraction measure.Item On arithmetic progressions in model sets(2022) Klick, Anna; Strungaru, Nicolae; Tcaciuc, AdiWe establish the existence of arbitrary-length arithmetic progressions in model sets and Meyer sets in Euclidean d-space. We prove a van der Waerden-type theorem for Meyer sets. We show that subsets of Meyer sets with positive density and pure point diffraction contain arithmetic progressions of arbitrary length.Item On higher dimensional arithmetic progressions in Meyer sets(2023) Klick, Anna; Strungaru, NicolaeIn this paper we study the existence of higher dimensional arithmetic progression in Meyer sets. We show that the case when the ratios are linearly dependent over $\ZZ$ is trivial, and focus on arithmetic progressions for which the ratios are linearly independent. Given a Meyer set Λ and a fully Euclidean model set $\oplam(W)$ with the property that finitely many translates of $\oplam(W)$ cover Λ, we prove that we can find higher dimensional arithmetic progressions of arbitrary length with k linearly independent ratios in Λ if and only if k is at most the rank of the $\ZZ$-module generated by $\oplam(W)$. We use this result to characterize the Meyer sets which are subsets of fully Euclidean model sets.