Spectral Correspondences for Rank One Locally Symmetric Spaces -- The Case of Exceptional Parameters
C. Arends, J. Hilgert, ArXiv:2112.11073 (2021).
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Arends, ChristianLibreCat;
Hilgert, Joachim
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Abstract
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.
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Journal Title
arXiv:2112.11073
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60
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Cite this
Arends C, Hilgert J. Spectral Correspondences for Rank One Locally Symmetric Spaces -- The Case of Exceptional Parameters. arXiv:211211073. Published online 2021.
Arends, C., & Hilgert, J. (2021). Spectral Correspondences for Rank One Locally Symmetric Spaces -- The Case of Exceptional Parameters. In arXiv:2112.11073.
@article{Arends_Hilgert_2021, title={Spectral Correspondences for Rank One Locally Symmetric Spaces -- The Case of Exceptional Parameters}, journal={arXiv:2112.11073}, author={Arends, Christian and Hilgert, Joachim}, year={2021} }
Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank One Locally Symmetric Spaces -- The Case of Exceptional Parameters.” ArXiv:2112.11073, 2021.
C. Arends and J. Hilgert, “Spectral Correspondences for Rank One Locally Symmetric Spaces -- The Case of Exceptional Parameters,” arXiv:2112.11073. 2021.
Arends, Christian, and Joachim Hilgert. “Spectral Correspondences for Rank One Locally Symmetric Spaces -- The Case of Exceptional Parameters.” ArXiv:2112.11073, 2021.