Spectral properties of substitutions on compact alphabets

Mañibo CN, Rust D, Walton JJ (2023)
Bulletin of the London Mathematical Society 55(5): 2425-2445.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Mañibo, Chrizaldy NeilUniBi; Rust, Dan; Walton, James J.
Abstract / Bemerkung
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.
Erscheinungsjahr
2023
Zeitschriftentitel
Bulletin of the London Mathematical Society
Band
55
Ausgabe
5
Seite(n)
2425 - 2445
ISSN
0024-6093
eISSN
1469-2120
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2980535

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Mañibo CN, Rust D, Walton JJ. Spectral properties of substitutions on compact alphabets. Bulletin of the London Mathematical Society . 2023;55(5):2425-2445.
Mañibo, C. N., Rust, D., & Walton, J. J. (2023). Spectral properties of substitutions on compact alphabets. Bulletin of the London Mathematical Society , 55(5), 2425-2445. https://doi.org/10.1112/blms.12872
Mañibo, Chrizaldy Neil, Rust, Dan, and Walton, James J. 2023. “Spectral properties of substitutions on compact alphabets”. Bulletin of the London Mathematical Society 55 (5): 2425-2445.
Mañibo, C. N., Rust, D., and Walton, J. J. (2023). Spectral properties of substitutions on compact alphabets. Bulletin of the London Mathematical Society 55, 2425-2445.
Mañibo, C.N., Rust, D., & Walton, J.J., 2023. Spectral properties of substitutions on compact alphabets. Bulletin of the London Mathematical Society , 55(5), p 2425-2445.
C.N. Mañibo, D. Rust, and J.J. Walton, “Spectral properties of substitutions on compact alphabets”, Bulletin of the London Mathematical Society , vol. 55, 2023, pp. 2425-2445.
Mañibo, C.N., Rust, D., Walton, J.J.: Spectral properties of substitutions on compact alphabets. Bulletin of the London Mathematical Society . 55, 2425-2445 (2023).
Mañibo, Chrizaldy Neil, Rust, Dan, and Walton, James J. “Spectral properties of substitutions on compact alphabets”. Bulletin of the London Mathematical Society 55.5 (2023): 2425-2445.
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2024-02-06T07:29:55Z
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