1 citations · 2 across the 6 of their papers we have counts for
6 papers
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…
Explicit Hilbert spaces for the unitary dual of rank one orthogonal groups and applications
Christian Arends, Frederik Bang-Jensen, Jan Frahm
We realize all irreducible unitary representations of the group on explicit Hilbert spaces of vector-valued -functions on .…
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…
Spectral Correspondences for Rank One Locally Symmetric Spaces -- The Case of Exceptional Parameters
Christian Arends, Joachim Hilgert
In this paper we complete the program of relating the Laplace spectrum for rank one compact locally symmetric spaces with the first band Ruelle-Pollicott resonances of the geodesic…