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

Author
Richard, Christoph
Strungaru, Nicolae
Faculty Advisor
Date
2017
Keywords
Fourier analysis , Bochner's theorem , pure point diffraction
Abstract (summary)
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.
Publication Information
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
DOI
Notes
Item Type
Report
Language
English
Rights
All Rights Reserved