Pure point diffractive substitution Delone sets have the Meyer property

Details Pure point diffractive substitution Delone sets have the Meyer property Pure point diffractive substitution Delone sets have the Meyer property

2005-10-18

arxiv.org/abs/math/0510389v2

Discrete Comput. Geom. 39 (2008), no. 1-3, 319--338

Mathematics

Dynamical Systems

22 pages; minor revision after referee reports; to appear in Discrete and Computational Geometry

Scientific paper

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.

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