Pure point diffractive substitution Delone sets have the Meyer property
Dynamical Systems
2011-07-20 v2
Abstract
We prove that a primitive substitution Delone set, which is pure point diffractive, is a Meyer set. This answers a question of J. C. Lagarias. We also show that for primitive substitution Delone sets, being a Meyer set is equivalent to having a relatively dense set of Bragg peaks. The proof is based on tiling dynamical systems and the connection between the diffraction and dynamical spectra.
Cite
@article{arxiv.math/0510389,
title = {Pure point diffractive substitution Delone sets have the Meyer property},
author = {Jeong-Yup Lee and Boris Solomyak},
journal= {arXiv preprint arXiv:math/0510389},
year = {2011}
}
Comments
22 pages; minor revision after referee reports; to appear in Discrete and Computational Geometry