Pure Point Diffractive Substitution Delone Sets Have the Meyer Property

Research paper by Jeong-Yup Lee, Boris Solomyak

Indexed on: 05 Mar '08Published on: 05 Mar '08Published in: Discrete & Computational Geometry


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.