A short guide to pure point diffraction in cut-and-project sets
Fourier analysis, Bochner's theorem, pure point diffraction
We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem from Fourier analysis. This clarifies a common view that the diffraction of a quasicrystal is determined by the diffraction of its underlying lattice. To illustrate our approach, we will also treat a number of well-known explicitly solvable examples.
Richard, C., & Strungaru, N. (2017). A short guide to pure point diffraction in cut-and-project sets. arXiv:1606.08831v2. https://arxiv.org/abs/1606.08831
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