Determining pure discrete spectrum for some self-affine tilings
Shigeki Akiyama, Franz Gähler, Jeong-Yup Lee
Abstract
By the algorithm implemented in the paper by Akiyama-Lee
[Adv. Math. 226(4):2855 13;2883, 2011] 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 Kenyon
[Geom. Func. Anal. 6:471 13;488, 1996].
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