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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.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.indag.2018.05.009
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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.

Item Type: Journal Item
Copyright Holders: 2018 Royal Dutch Mathematical Society (KWG)
ISSN: 0019-3577
Keywords: substitution dynamical system; spectral measure; absolute continuity; Lebesgue spectrum
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
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Item ID: 54841
Depositing User: Uwe Grimm
Date Deposited: 03 May 2018 10:33
Last Modified: 26 May 2019 15:02
URI: http://oro.open.ac.uk/id/eprint/54841
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