Author
Daniel Lenz
Other affiliations: Schiller International University, Goethe University Frankfurt, Hebrew University of Jerusalem ...read more
Bio: Daniel Lenz is an academic researcher from University of Jena. The author has contributed to research in topics: Ergodic theory & Dynamical systems theory. The author has an hindex of 38, co-authored 217 publications receiving 5243 citations. Previous affiliations of Daniel Lenz include Schiller International University & Goethe University Frankfurt.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the authors consider topological dynamical systems that arise 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.
Abstract: Certain topological dynamical systems that arise from actions of -compact locally compact Abelian groups on compact spaces of translation bounded measures are considered. Such a measure dynamical system is shown to have a pure point dynamical spectrum if and only if its diffraction spectrum is pure point.
215 citations
TL;DR: In this article, a sufficient geometric condition for essential selfadjointness was given and the generators of the associated semigroups were explicitly determined for graphs and networks via regular Dirichlet forms.
Abstract: We study Laplacians on graphs and networks via regular Dirichlet forms. We give a sufficient geometric condition for essential selfadjointness and explicitly determine the generators of the associated semigroups on all $\ell^p$, $1\leq p < \infty$, in this case. We characterize stochastic completeness thereby generalizing all earlier corresponding results for graph Laplacians. Finally, we study how stochastic completeness of a subgraph is related to stochastic completeness of the whole graph.
188 citations
Posted Content•
TL;DR: In this article, a sufficient geometric condition for essential selfadjointness was given and the generators of the associated semigroups were explicitly determined for graphs and networks via regular Dirichlet forms.
Abstract: We study Laplacians on graphs and networks via regular Dirichlet forms. We give a sufficient geometric condition for essential selfadjointness and explicitly determine the generators of the associated semigroups on all $\ell^p$, $1\leq p < \infty$, in this case. We characterize stochastic completeness thereby generalizing all earlier corresponding results for graph Laplacians. Finally, we study how stochastic completeness of a subgraph is related to stochastic completeness of the whole graph.
165 citations
TL;DR: In this paper, the authors discuss Laplacians on graphs in a framework of regular Dirichlet forms and focus on phenomena related to unboundedness of the LaplACians.
Abstract: We discuss Laplacians on graphs in a framework of regular Dirichlet forms. We focus on phenomena related to unboundedness of the Laplacians. This includes (failure of) essential selfadjointness, absence of essential spectrum and stochastic incompleteness.
164 citations
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.
Abstract: Certain topological dynamical systems are considered that arise from actions of $\sigma$-compact locally compact Abelian groups on compact spaces of translation bounded measures. Such a measure dynamical system is shown to have pure point dynamical spectrum if and only if its diffraction spectrum is pure point.
131 citations
Cited by
More filters
01 Jan 2016
TL;DR: The methods of modern mathematical physics is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
Abstract: Thank you very much for reading methods of modern mathematical physics. Maybe you have knowledge that, people have look numerous times for their favorite novels like this methods of modern mathematical physics, but end up in harmful downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious virus inside their desktop computer. methods of modern mathematical physics is available in our digital library an online access to it is set as public so you can download it instantly. Our books collection saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the methods of modern mathematical physics is universally compatible with any devices to read.
1,536 citations
438 citations