English

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

Mathematical Physics 2020-04-02 v2 math.MP Spectral Theory

Abstract

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.

Cite

@article{arxiv.1606.08831,
  title  = {A short guide to pure point diffraction in cut-and-project sets},
  author = {Christoph Richard and Nicolae Strungaru},
  journal= {arXiv preprint arXiv:1606.08831},
  year   = {2020}
}

Comments

25 pages, 3 figures, v2: presentation improved

R2 v1 2026-06-22T14:37:19.125Z