8 citations · 34 across the 19 of their papers we have counts for
28 papers
A Liouville Theorem for Domains in Graphs
Philipp Hake, Matthias Keller, Felix Pogorzelski +1
We show a Liouville theorem for domains in graphs with Dirichlet boundary conditions. More specifically, we characterize the non-existence of non-zero bounded harmonic functions. S…
Graphs at infinity: Liouville theorems, Recurrence and Characterization of Dirichlet forms
Matthias Keller, Daniel Lenz, Marcel Schmidt
We survey recent results on graphs and their Laplacians related to the behavior of the graph at large. In particular, we focus on Liouville theorems, recurrence and characterizatio…
Note on intrinsic metrics on graphs
Daniel Lenz, Marcel Schmidt, Felix Seifert
We study the set of intrinsic metrics on a given graph. This is a convex compact set and it carries a natural order. We investigate existence of largest elements with respect to th…
Harris' criterion and Hardy inequalites on graphs
Simon Murmann, Marcel Schmidt
In this paper we give a version of Harris' criterion for determining within on discrete spaces. Moreover, we provide a converse via Hardy inequalities involvi…
Recurrent and (strongly) resolvable graphs
Daniel Lenz, Simon Puchert, Marcel Schmidt
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric…
Boundary representations of intermediate forms between a regular Dirichlet form and its active main part
Matthias Keller, Daniel Lenz, Marcel Schmidt +2
We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet form is regular, we give a more…