3 papers
math.SP2026
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…
math.SP2026
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…
math.RT2024
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 .…