Determining pure discrete spectrum for some self-affine tilings

2014/03/03 by Shigeki Akiyama, Akiyama, Shigeki, Franz Gaehler +3
Mathematics · #52C23 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:52C23

paper · pdf · doi:10.48550/arxiv.1403.0362

4 figures

arxiv created 2014/10/14 · arxiv updated 2014/10/15

Abstract

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.

Related

• Pure discrete spectrum in substitution tiling spaces
• Pure discrete spectrum for a class of one-dimensional substitution tiling systems
• Pisot family self-affine tilings, discrete spectrum, and the Meyer property
• Pure Discrete Spectrum and Regular Model Sets in Unimodular Substitution Tilings on R^d
• Algorithm for determining pure pointedness of self-affine tilings