{"_id":"51204","status":"public","date_created":"2024-02-06T20:35:36Z","external_id":{"arxiv":["2402.02530"]},"author":[{"first_name":"Christopher","last_name":"Lutsko","full_name":"Lutsko, Christopher"},{"orcid":"0000-0002-9648-6919","id":"49178","first_name":"Tobias","full_name":"Weich, Tobias","last_name":"Weich"},{"orcid":"0000-0001-8893-2045","id":"45027","first_name":"Lasse Lennart","full_name":"Wolf, Lasse Lennart","last_name":"Wolf"}],"year":"2024","user_id":"45027","citation":{"short":"C. Lutsko, T. Weich, L.L. Wolf, ArXiv:2402.02530 (2024).","bibtex":"@article{Lutsko_Weich_Wolf_2024, title={Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces}, journal={arXiv:2402.02530}, author={Lutsko, Christopher and Weich, Tobias and Wolf, Lasse Lennart}, year={2024} }","ieee":"C. Lutsko, T. Weich, and L. L. Wolf, “Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces,” <i>arXiv:2402.02530</i>. 2024.","ama":"Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces. <i>arXiv:240202530</i>. Published online 2024.","mla":"Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally  Symmetric Spaces.” <i>ArXiv:2402.02530</i>, 2024.","chicago":"Lutsko, Christopher, Tobias Weich, and Lasse Lennart Wolf. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally  Symmetric Spaces.” <i>ArXiv:2402.02530</i>, 2024.","apa":"Lutsko, C., Weich, T., &#38; Wolf, L. L. (2024). Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces. In <i>arXiv:2402.02530</i>."},"type":"preprint","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"language":[{"iso":"eng"}],"date_updated":"2024-05-07T11:46:55Z","title":"Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces","publication":"arXiv:2402.02530","abstract":[{"text":"Given a real semisimple connected Lie group $G$ and a discrete torsion-free\r\nsubgroup $\\Gamma < G$ we prove a precise connection between growth rates of the\r\ngroup $\\Gamma$, polyhedral bounds on the joint spectrum of the ring of\r\ninvariant differential operators, and the decay of matrix coefficients. In\r\nparticular, this allows us to completely characterize temperedness of\r\n$L^2(\\Gamma\\backslash G)$ in this general setting.","lang":"eng"}]}