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TITLE Cut-and-Project Schemes for Pisot Family Substitution Tilings
KIAS AUTHORS Lee, Jeong-Yup
JOURNAL SYMMETRY-BASEL, 2018
ARCHIVE  
ABSTRACT We consider Pisot family substitution tilings in R-d whose dynamical spectrum is pure point. There are two cut-and-project schemes (CPSs) which arise naturally: one from the Pisot family property and the other from the pure point spectrum. The first CPS has an internal space R-m for some integer m is an element of N defined from the Pisot family property, and the second CPS has an internal space H that is an abstract space defined from the condition of the pure point spectrum. However, it is not known how these two CPSs are related. Here we provide a sufficient condition to make a connection between the two CPSs. For Pisot unimodular substitution tiling in R, the two CPSs turn out to be same due to the remark by Barge-Kwapisz.
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