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

Richard, Christoph; Strungaru, Nicolae

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

Author

Richard, Christoph

Strungaru, Nicolae

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

Item Type

Report

Language

English

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