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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2026 2verdicts
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For measures on a strip whose Fourier transform is a pure-point measure, the squared-amplitude measure has exponential growth, and the transform measure does too when points of the support in intervals of fixed length are linearly independent over the integers.
citing papers explorer
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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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Some properties of Fourier quasicrystals and measures on a strip
For measures on a strip whose Fourier transform is a pure-point measure, the squared-amplitude measure has exponential growth, and the transform measure does too when points of the support in intervals of fixed length are linearly independent over the integers.