Spectral theory of spin substitutions
Frank NP, Mañibo CN (2022)
Discrete and Continuous Dynamical Systems. Series A.
Zeitschriftenaufsatz
| E-Veröff. vor dem Druck | Englisch
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Autor*in
Frank, Natalie Priebe;
Mañibo, Chrizaldy NeilUniBi
Einrichtung
Abstract / Bemerkung
We introduce substitutions in Z(m) which have non-rectangular domains based on an endomorphism Q of Z(m) and a set D of coset representatives of Z(m)/QZ(m), which we call digit substitutions. Using a finite abelian 'spin' group we define 'spin digit substitutions' and their subshifts (sigma, Z(m)). Conditions under which the subshift is measure-theoretically isomorphic to a group extension of an m-dimensional odometer are given, inducing a complete decomposition of the function space L-2(sigma, mu). This enables the use of group characters in G over cap to derive substitutive factors and analyze the spectra of specific subspaces. We provide general sufficient criteria for the existence of pure point, absolutely continuous, and singular continuous spectral measures, together with some bounds on their spectral multiplicity.
Stichworte
Dynamical spectrum;
diffraction;
substitution tilings;
group extensions
Erscheinungsjahr
2022
Zeitschriftentitel
Discrete and Continuous Dynamical Systems. Series A
ISSN
1078-0947
eISSN
1553-5231
Page URI
https://pub.uni-bielefeld.de/record/2965253
Zitieren
Frank NP, Mañibo CN. Spectral theory of spin substitutions. Discrete and Continuous Dynamical Systems. Series A. 2022.
Frank, N. P., & Mañibo, C. N. (2022). Spectral theory of spin substitutions. Discrete and Continuous Dynamical Systems. Series A. https://doi.org/10.3934/dcds.2022105
Frank, Natalie Priebe, and Mañibo, Chrizaldy Neil. 2022. “Spectral theory of spin substitutions”. Discrete and Continuous Dynamical Systems. Series A.
Frank, N. P., and Mañibo, C. N. (2022). Spectral theory of spin substitutions. Discrete and Continuous Dynamical Systems. Series A.
Frank, N.P., & Mañibo, C.N., 2022. Spectral theory of spin substitutions. Discrete and Continuous Dynamical Systems. Series A.
N.P. Frank and C.N. Mañibo, “Spectral theory of spin substitutions”, Discrete and Continuous Dynamical Systems. Series A, 2022.
Frank, N.P., Mañibo, C.N.: Spectral theory of spin substitutions. Discrete and Continuous Dynamical Systems. Series A. (2022).
Frank, Natalie Priebe, and Mañibo, Chrizaldy Neil. “Spectral theory of spin substitutions”. Discrete and Continuous Dynamical Systems. Series A (2022).
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