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Pure point diffractive substitution Delone sets have the Meyer property

Jeong-Yup Lee·Boris Solomyak
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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.

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Jeong-Yup Lee, Boris Solomyak. 2006-05-05. Pure point diffractive substitution Delone sets have the Meyer property. https://arxiv.org/abs/math/0510389

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