Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings

DOI10.25537/dm.2020v25.2303-2337zbMath1462.11060arXiv1907.11012OpenAlexW2963567417MaRDI QIDQ2218100

Uwe Grimm, Michael Baake

Publication date: 12 January 2021

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.11012

zbMATH Keywords

Rauzy fractalmodel setmathematical diffractionFourier cocycleinflation tiling

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Fractals (28A80) Symbolic dynamics (37B10) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Harmonic analysis and almost periodicity in probabilistic number theory (11K70) Renormalization of holomorphic dynamical systems (37F25)

Related Items (9)

Eberlein decomposition for PV inflation systems ⋮ Spectral theory of regular sequences ⋮ Mixing properties and entropy bounds of a family of Pisot random substitutions ⋮ Purity results for some arithmetically defined measures ⋮ On the (dis)continuity of the Fourier transform of measures ⋮ Multidimensional continued fractions and symbolic codings of toral translations ⋮ Why do (weak) Meyer sets diffract? ⋮ Zeckendorf representations and mixing properties of sequences ⋮ Three variations on a theme by Fibonacci

Uses Software

• OEIS

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