Determining pure discrete spectrum for some self-affine tilings

By the algorithm implemented in the paper [2] by Akiyama-Lee and some of its predecessors, we have examined the pure discreteness of the spectrum for all irreducible Pisot substitutions of trace less than or equal to $2$, and some cases of planar tilings generated by boundary substitutions due to th...

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Bibliographic Details
Main Authors Akiyama, Shigeki, Gaehler, Franz, Lee, Jeong-Yup
Format Journal Article
LanguageEnglish
Published 03.03.2014
Subjects
Mathematics - Metric Geometry
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Summary:By the algorithm implemented in the paper [2] by Akiyama-Lee and some of its predecessors, we have examined the pure discreteness of the spectrum for all irreducible Pisot substitutions of trace less than or equal to $2$, and some cases of planar tilings generated by boundary substitutions due to the paper [17] by Kenyon.
DOI:10.48550/arxiv.1403.0362