4 citations · 5 across the 4 of their papers we have counts for
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Elliptic operators on planar graphs: Unique continuation for eigenfunctions and nonpositive curvature
S. Klassert, D. Lenz, N. Peyerimhoff +1
This paper is concerned with elliptic operators on plane tessellations. We show that such an operator does not admit a compactly supported eigenfunction, if the combinatorial curva…
Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians
Daniel Lenz, Peter Stollmann
We show that geometric disorder leads to purely singular continuous spectrum generically. The main input is a result of Simon known as the ``Wonderland theorem''. Here, we provide…
An ergodic theorem for Delone dynamical systems and existence of the integrated density of states
Daniel Lenz, Peter Stollmann
We study strictly ergodic Delone dynamical systems and prove an ergodic theorem for Banach space valued functions on the associated set of pattern classes. As an application, we pr…
Algebras of random operators associated to Delone dynamical systems
D. Lenz, P. Stollmann
We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of th…
Delone dynamical systems and associated random operators
Daniel Lenz, Peter Stollmann
We carry out a careful study of basic topological and ergodic features of Delone dynamical systems. We then investigate the associated topological groupoids and in particular their…