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Mañibo, Neil; Rust, Dan and Walton, James J.
(2023).
DOI: https://doi.org/10.1112/blms.12872
Abstract
We consider substitutions on compact alphabets and provide sufficient conditions for the diffraction to be pure point, absolutely continuous and singular continuous. This allows one to construct examples for which the Koopman operator on the associated function space has specific spectral components. For abelian bijective substitutions, we provide a dichotomy result regarding the spectral type of the diffraction. We also provide the first example of a substitution that has countably infinite Lebesgue spectral components and countably infinite singular continuous components. Lastly, we give a non-constant length substitution on a countably infinite alphabet that gives rise to substitutive Delone sets of infinite type. This extends the spectral theory of substitutions on finite alphabets and Delone sets of finite type with inflation symmetry.
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About
- Item ORO ID
- 88589
- Item Type
- Journal Item
- ISSN
- 1469-2120
- Project Funding Details
-
Funded Project Name Project ID Funding Body Postdoctoral Researchers International Mobility Experience Not Set German Academic Exchange Service (DAAD) Collaborative Research Centre (CRC 1283) CRC1283 German Research Foundation - Keywords
- substitutions; infinite alphabets; positive operators; quasi-compactness; unique ergodicity
- 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
- © 2023 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society.
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- Depositing User
- Dan Rust
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