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.
Quasicrystals and Poisson's summation formula
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abstract
We characterize the measures on R which have both their support and spectrum uniformly discrete. A similar result is obtained in R^n for positive measures.
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2026 1verdicts
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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.