27 citations · 201 across the 34 of their papers we have counts for
38 papers
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…
Quantum-Classical Correspondences for Locally Symmetric Spaces
Joachim Hilgert
We review the status of a program, outlined and motivated in the introduction, for the study of correspondences between spectral invariants of partially hyperbolic flows on locally…
Quantization in fibering polarizations, Mabuchi rays and geometric Peter--Weyl theorem
Thomas Baier, Joachim Hilgert, Oğuzhan Kaya +2
In this paper we use techniques of geometric quantization to give a geometric interpretation of the Peter--Weyl theorem. We present a novel approach to half-form corrected geometri…
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…
Higher rank quantum-classical correspondence
Joachim Hilgert, Tobias Weich, Lasse L. Wolf
For a compact Riemannian locally symmetric space of arbitrary rank we determine the location of certain Ruelle-Taylor resonances for the Weyl chamber action. We p…