Inter-model sets in Rd are model sets
Faculty Advisor
Date
2024
Keywords
model sets, substitution point sets, torus parametrisation
Abstract (summary)
We show that any union of finitely many shifted model sets from a given cut-and-project scheme is a model set in some modified cut-and-project scheme. Restricting to direct space Rd, we show that any inter-model set is a model set in some modified cut-and-project scheme with second countable internal space. In both cases, the window in the modified cut-and-project scheme inherits the topological and measure-theoretic properties of the original windows.
Publication Information
Richard, C., & Strungaru, N. (2024). Inter-model sets in Rd are model sets. Indagationes Mathematicae 35(5), 865-889. https://doi.org/10.1016/j.indag.2023.06.007
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Article
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