4 papers · 1 filter
Patterson-Sullivan distributions of finite regular graphs
Christian Arends, Guendalina Palmirotta
On finite regular graphs, we construct Patterson-Sullivan distributions associated with eigenfunctions of the discrete Laplace operator via their boundary values on the phase space…
Resonances on geometrically finite graphs
Christian Arends, Carsten Peterson, Tobias Weich
In analogy with the spectral theory of geometrically finite hyperbolic manifolds, we initiate the study of resonances on geometrically finite (q+1)-regular graphs of groups. We pro…
A Pairing Formula for Resonant States on Finite Regular Graphs
Christian Arends, Jan Frahm, Joachim Hilgert
On a finite regular graph, (co)resonant states are eigendistributions of the transfer operator associated to the shift on one-sided infinite non-backtracking paths. We introduce tw…
Edge Laplacians and Edge Poisson Transforms for Graphs
Christian Arends, Jan Frahm, Joachim Hilgert
For a finite graph, we establish natural isomorphisms between eigenspaces of a Laplace operator acting on functions on the edges and eigenspaces of a transfer operator acting on fu…