Determining pure discrete spectrum for some self-affine tilings

Shigeki Akiyama (1) , Franz Gähler (2) , Jeong-Yup Lee (3)

1 Institute of Mathematics, University of Tsukuba
2 Fakultät für Mathematik = Faculty of Mathematics [Bielefeld]
3 Department of Mathematics Education [Kwandong]

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].

Mots clés: Pisot substitution; pure discrete spectrum; self-affine tiling

Domaines: Mathématique discrète [cs.DM]

Shigeki Akiyama, Franz Gähler, Jeong-Yup Lee. Determining pure discrete spectrum for some self-affine tilings. Discrete Mathematics and Theoretical Computer Science, 2014, Vol. 16 no. 3 (3), pp.305--316. ⟨10.46298/dmtcs.2089⟩. ⟨hal-01188903⟩