Substitution-based structures with absolutely continuous spectrum

Chan, Lax; Grimm, Uwe and Short, Ian (2018). Substitution-based structures with absolutely continuous spectrum. Indagationes Mathematicae, 29(4) pp. 1072–1086.

DOI: https://doi.org/10.1016/j.indag.2018.05.009

Abstract

By generalising Rudin’s construction of an aperiodic sequence, we derive new substitution-based structures which have a purely absolutely continuous diffraction measure and a mixed dynamical spectrum, with absolutely continuous and pure point parts. We discuss several examples, including a construction based on Fourier matrices which yields constant-length substitutions for any length.

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About

• Item ORO ID
• 54841
• Item Type
• Journal Item
• ISSN
• 0019-3577
• Keywords
• substitution dynamical system; spectral measure; absolute continuity; Lebesgue spectrum
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2018 Royal Dutch Mathematical Society (KWG)
• Related URLs
• • https://arxiv.org/abs/1706.05289(Other)
• Depositing User
• Uwe Grimm