Work

Pure point diffractive substitution Delone sets have the Meyer property

Year: 2005

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.math/0510389

Authors: Lee, Jeong-Yup, Solomyak, Boris

Language: English

Topic: Quasicrystal Structures and Properties

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, University of Washington, Weizmann Institute of Science, Natural Sciences and Engineering Research Council of Canada

Award: Measures, Dimension, and Ergodic Theory

OpenAlex ID: W4306725375

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