27 citations · 201 across the 34 of their papers we have counts for
6 papers · 1 filter
Spectral correspondences for finite graphs without dead ends
Kai-Uwe Bux, Joachim Hilgert, Tobias Weich
We compare the spectral properties of two kinds of linear operators characterizing the (classical) geodesic flow and its quantization on connected locally finite graphs without dea…
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…
Poisson Transforms for Trees of Bounded Degree
Kai-Uwe Bux, Joachim Hilgert, Tobias Weich
We introduce a parameterized family of Poisson transforms on trees of bounded degree, construct explicit inverses for generic parameters, and characterize moderate growth of Laplac…
Resonances and Scattering Poles in Symmetric Spaces of Rank One
Sönke Hansen, Joachim Hilgert, Aprameyan Parthasarathy
We relate resolvent and scattering kernels for the Laplace operator on Riemannian symmetric spaces of rank one via boundary values in the sense of Kashiwara-Oshima. From this, we d…
Patterson--Sullivan distributions in higher rank
Sönke Hansen, Joachim Hilgert, Michael Schröder
For a compact locally symmetric space $\XG$ of non-positive curvature, we consider sequences of normalized joint eigenfunctions which belong to the principal spectrum of the algebr…
Patterson--Sullivan distributions for rank one symmetric spaces of the noncompact type
Joachim Hilgert, Michael Schroeder
There is a remarkable relation between two kinds of phase space distributions associated to eigenfunctions of the Laplacian of a compact hyperbolic manifold: It was observed in \ci…