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Characterizations of model sets by dynamical systems
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abstract
It is shown how regular model sets can be characterized in terms of regularity properties of their associated dynamical systems. The proof proceeds in two steps. First, we characterize regular model sets in terms of a certain map $\beta$ and then relate the properties of $\beta$ to ones of the underlying dynamical system. As a by-product, we can show that regular model sets are, in a suitable sense, as close to periodic sets as possible among repetitive aperiodic sets.
Forward citations
Cited by 2 Pith papers
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On almost periodicity in crystalline measures
Crystalline measures are almost periodic if and only if translation bounded; new constructions resolve Meyer's and Favorov's questions by exhibiting crystalline measures that are not translation bounded even as distributions.
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Pure point measures with sparse support and sparse Fourier--Bohr support
Doubly sparse measures on second countable locally compact Abelian groups are shown to be supported on finitely many translates of a lattice with trigonometric polynomial amplitudes.
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