This paper reviews the mathematical connections among continuity of the diffraction spectrum, uniform vanishing of Fourier-Bohr coefficients, and consistent phase frequency.
Pure Point Dynamical and Diffraction Spectra
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abstract
We show that for multi-colored Delone point sets with finite local complexity and uniform cluster frequencies the notions of pure point diffraction and pure point dynamical spectrum are equivalent.
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2026 1verdicts
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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.