TY - JOUR AU - Arends, Christian AU - Wolf, Lasse Lennart AU - Meinecke, Jasmin AU - Barkhofen, Sonja AU - Weich, Tobias AU - Bartley, Tim ID - 52876 IS - 1 JF - Physical Review Research KW - General Physics and Astronomy SN - 2643-1564 TI - Decomposing large unitaries into multimode devices of arbitrary size VL - 6 ER - TY - JOUR AB - 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. AU - Arends, Christian AU - Hilgert, Joachim ID - 31210 JF - Journal de l’École polytechnique — Mathématiques KW - Ruelle resonances KW - Poisson transforms KW - locally symmetric spaces KW - principal series representations SN - 2429-7100 TI - Spectral correspondences for rank one locally symmetric spaces: the case of exceptional parameters VL - 10 ER -