Modulated crystals and almost periodic measures
arXiv:1907.07017 · doi:10.1007/s11005-020-01337-2
Abstract
Modulated crystals and quasicrystals can simultaneously be described as modulated quasicrystals, a class of point sets introduced by de Bruijn in 1987. With appropriate modulation functions, modulated quasicrystals themselves constitute a substantial subclass of strongly almost periodic point measures. We re-analyse these structures using methods from modern mathematical diffraction theory, thereby providing a coherent view over that class. Similarly to de Bruijn's analysis, we find stability with respect to almost periodic modulations.
arXiv comment33 pages, 1 figure, v2: appendix shortened and restructured, other minor changes
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