Pure Point Dynamical and Diffraction Spectra
TL;DR: In this article, it was shown that for multi-colored Delone point sets with finite local complexity and uniform cluster frequencies, the notions of pure point diffraction and pure point dynamical spectrum are equivalent.
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Abstract: We show that for multi-colored Delone point sets with finite local complexity and uniform cluster frequencies the notions of pure point diffraction and pure point dynamical spectrum are equivalent.
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Citations
Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra
Michael Baake,Daniel Lenz +1 more
TL;DR: In this paper, the authors consider topological dynamical systems arising from locally compact Abelian groups on compact spaces of translation bounded measures and show that such a system has a pure point dynamical spectrum if and only if its diffraction spectrum is pure point.
174
Characterization of model sets by dynamical systems
TL;DR: In this paper, it is shown how regular model sets can be characterized in terms of the regularity properties of their associated dynamical systems, and that regular models are as close to periodic sets as possible among repetitive aperiodic sets.
138
Characterizations of model sets by dynamical systems
TL;DR: In this article, it is shown how regular model sets can be characterized in terms of regularity properties of their associated dynamical systems, and that regular models are as close to periodic sets as possible among repetitive aperiodic sets.
137
Pure Point spectrum for measure dynamical systems on locally compact Abelian groups
Daniel Lenz,Nicolae Strungaru +1 more
TL;DR: In this article, the authors show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact Abelian groups.
87
Consequences of Pure Point Diffraction Spectra for Multiset Substitution Systems
TL;DR: The main result is that for lattice substitution multiset systems (in arbitrary dimensions), being a regular model set is not only sufficient for having pure point spectrum—a known fact—but is also necessary.
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Substitution dynamical systems, spectral analysis
Martine Queffélec
- 01 Jan 1987
TL;DR: The Banach Algebra (T) as mentioned in this paper is a generalization of the Spectral Theory of Unitary Operators (SOTO) of Dynamical Systems (DOS).
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Pointwise theorems for amenable groups
TL;DR: In this paper, the pointwise ergodic theorem for general locally compact amenable groups along Folner sequences was shown to hold for all amenable group along folner sequences that obey some restrictions.
349
Consequences of Pure Point Diffraction Spectra for Multiset Substitution Systems
TL;DR: In this paper, it was shown that for lattice substitution multiset systems, being a regular model set is not only sufficient for having pure point spectrum, but also necessary.
Weighted Dirac combs with pure point diffraction
Michael Baake,Robert V. Moody +1 more
TL;DR: In this article, a class of translation bounded complex measures, which have the form of weighted Dirac combs, on locally compact Abelian groups is investigated, and a sufficient set of conditions to ensure that the diffraction measure is a pure point measure is presented.