Modulated crystals and almost periodic measures

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.

33 pages, 1 figure, v2: appendix shortened and restructured, other minor changes

References in corpus (3)

• Pure point diffraction and cut and project schemes for measures: The smooth case
• On the Fourier Analysis of Measures with Meyer Set Support
• Periods and factors of weak model sets

Cited by in corpus (4)

• Linear repetitivity beyond abelian groups
• Inter model sets in ${\mathbb{R}}^d$ are model sets
• On eigenmeasures under Fourier transform
• Measures, modular forms, and summation formulas of Poisson type