A short guide to pure point diffraction in cut-and-project sets

Abstract

We briefly review the diffraction of quasicrystals and then give an\nelementary alternative proof of the diffraction formula for regular\ncut-and-project sets, which is based on Bochner's theorem from Fourier\nanalysis. This clarifies a common view that the diffraction of a quasicrystal\nis determined by the diffraction of its underlying lattice. To illustrate our\napproach, we will also treat a number of well-known explicitly solvable\nexamples.\n