On weak model sets of extremal density

Baake M, Huck C, Strungaru N (2017)
Indagationes Mathematicae. New Series 28(1): 3-31.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Abstract / Bemerkung
The theory of regular model sets is highly developed, but does not cover examples such as the visible lattice points, the kth power-free integers, or related systems. They belong to the class of weak model sets, where the window may have a boundary of positive measure, or even consists of boundary only. The latter phenomena are related to the topological entropy of the corresponding dynamical system and to various other unusual properties. Under a rather natural extremality assumption on the density of the weak model set, we establish its pure point diffraction nature. We derive an explicit formula that can be seen as the generalisation of the case of regular model sets. Furthermore, the corresponding natural patch frequency measure is shown to be ergodic. Since weak model sets of extremal density are generic for this measure, one obtains that the dynamical spectrum of the hull is pure point as well. (C) 2016 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
Erscheinungsjahr
2017
Zeitschriftentitel
Indagationes Mathematicae. New Series
Band
28
Ausgabe
1
Seite(n)
3-31
ISSN
0019-3577
eISSN
1872-6100
Page URI
https://pub.uni-bielefeld.de/record/2909441

Zitieren

Baake M, Huck C, Strungaru N. On weak model sets of extremal density. Indagationes Mathematicae. New Series. 2017;28(1):3-31.
Baake, M., Huck, C., & Strungaru, N. (2017). On weak model sets of extremal density. Indagationes Mathematicae. New Series, 28(1), 3-31. https://doi.org/10.1016/j.indag.2016.11.002
Baake, M., Huck, C., and Strungaru, N. (2017). On weak model sets of extremal density. Indagationes Mathematicae. New Series 28, 3-31.
Baake, M., Huck, C., & Strungaru, N., 2017. On weak model sets of extremal density. Indagationes Mathematicae. New Series, 28(1), p 3-31.
M. Baake, C. Huck, and N. Strungaru, “On weak model sets of extremal density”, Indagationes Mathematicae. New Series, vol. 28, 2017, pp. 3-31.
Baake, M., Huck, C., Strungaru, N.: On weak model sets of extremal density. Indagationes Mathematicae. New Series. 28, 3-31 (2017).
Baake, Michael, Huck, Christian, and Strungaru, Nicolae. “On weak model sets of extremal density”. Indagationes Mathematicae. New Series 28.1 (2017): 3-31.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar