Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings

Substitution tilings with pure discrete spectrum are characterized as regular model sets whose cut-and-project scheme has an internal space that is a product of a Euclidean space and a profinite group. Assumptions made here are that the expansion map of the substitution is diagonalizable and its eig...

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Autor principal: Lee, Jeong-Yup
Formato: Online Artículo Texto
Lenguaje:English
Publicado: International Union of Crystallography 2022
Materias:
Research Papers
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9434600/
https://www.ncbi.nlm.nih.gov/pubmed/36047401
http://dx.doi.org/10.1107/S2053273322006714
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author Lee, Jeong-Yup
author_facet Lee, Jeong-Yup
author_sort Lee, Jeong-Yup
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description Substitution tilings with pure discrete spectrum are characterized as regular model sets whose cut-and-project scheme has an internal space that is a product of a Euclidean space and a profinite group. Assumptions made here are that the expansion map of the substitution is diagonalizable and its eigenvalues are all algebraically conjugate with the same multiplicity. A difference from the result of Lee et al. [Acta Cryst. (2020), A76, 600–610] is that unimodularity is no longer assumed in this paper.
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spelling pubmed-94346002022-09-19 Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings Lee, Jeong-Yup Acta Crystallogr A Found Adv Research Papers Substitution tilings with pure discrete spectrum are characterized as regular model sets whose cut-and-project scheme has an internal space that is a product of a Euclidean space and a profinite group. Assumptions made here are that the expansion map of the substitution is diagonalizable and its eigenvalues are all algebraically conjugate with the same multiplicity. A difference from the result of Lee et al. [Acta Cryst. (2020), A76, 600–610] is that unimodularity is no longer assumed in this paper. International Union of Crystallography 2022-08-12 /pmc/articles/PMC9434600/ /pubmed/36047401 http://dx.doi.org/10.1107/S2053273322006714 Text en © Jeong-Yup Lee 2022 https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.
spellingShingle Research Papers
Lee, Jeong-Yup
Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings
title Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings
title_full Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings
title_fullStr Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings
title_full_unstemmed Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings
title_short Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings
title_sort pure discrete spectrum and regular model sets on some non-unimodular substitution tilings
topic Research Papers
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9434600/
https://www.ncbi.nlm.nih.gov/pubmed/36047401
http://dx.doi.org/10.1107/S2053273322006714
work_keys_str_mv AT leejeongyup purediscretespectrumandregularmodelsetsonsomenonunimodularsubstitutiontilings

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