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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This paper reviews the mathematical connections among continuity of the diffraction spectrum, uniform vanishing of Fourier-Bohr coefficients, and consistent phase frequency.
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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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Continuous diffraction spectrum and the uniform vanishing of Fourier--Bohr coefficients
This paper reviews the mathematical connections among continuity of the diffraction spectrum, uniform vanishing of Fourier-Bohr coefficients, and consistent phase frequency.