Sie haben Javascript deaktiviert!
Sie haben versucht eine Funktion zu nutzen, die nur mit Javascript möglich ist. Um sämtliche Funktionalitäten unserer Internetseite zu nutzen, aktivieren Sie bitte Javascript in Ihrem Browser.

Paderborn University in February 2023 Show image information

Paderborn University in February 2023

Photo: Paderborn University, Hannah Brauckhoff

Christian Arends

 Christian Arends

Lie Theory

Former - Doktorand

Spectral Analysis


Open list in Research Information System


Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters

C. Arends, J. Hilgert, Journal de l’École polytechnique — Mathématiques (2023), 10, pp. 335-403

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 flow on its sphere bundle. This program was started by Flaminio and Forni for hyperbolic surfaces, continued by Dyatlov, Faure and Guillarmou for real hyperbolic spaces and by Guillarmou, Hilgert and Weich for general rank one spaces. Except for the case of hyperbolic surfaces a countable set of exceptional spectral parameters always left untreated since the corresponding Poisson transforms are neither injective nor surjective. We use vector valued Poisson transforms to treat also the exceptional spectral parameters. For surfaces the exceptional spectral parameters lead to discrete series representations of $\mathrm{SL}(2,\mathbb R)$. In higher dimensions the situation is more complicated, but can be described completely.

Open list in Research Information System

The University for the Information Society