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