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Dense Dirac combs in Euclidean space with pure point diffraction
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Regular model sets, describing the point positions of ideal quasicrystallographic tilings, are mathematical models of quasicrystals. An important result in mathematical diffraction theory of regular model sets, which are defined on locally compact Abelian groups, is the pure pointedness of the diffraction spectrum. We derive an extension of this result, valid for dense point sets in Euclidean space, which is motivated by the study of quasicrystallographic random tilings.
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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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