Pure point diffractive substitution delone sets have the meyer property

Jeong Yup Lee, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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.

Original languageEnglish
Pages (from-to)319-338
Number of pages20
JournalDiscrete and Computational Geometry
Issue number1-3
StatePublished - Mar 2008
Externally publishedYes

Bibliographical note

Funding Information:
The first author acknowledges support from the NSERC post-doctoral fellowship and thanks the University of Washington and the University of Victoria for being the host universities of the fellowship. The second author is grateful to the Weizmann Institute of Science where he was a Rosi and Max Varon Visiting Professor when this work was completed. He was also supported in part by NSF Grant DMS 0355187.


Dive into the research topics of 'Pure point diffractive substitution delone sets have the meyer property'. Together they form a unique fingerprint.

Cite this