[{"user_id":"30905","department":[{"_id":"93"}],"project":[{"_id":"161","name":"RegLie: Regularität von Lie-Gruppen und Lie's Dritter Satz (RegLie)"}],"_id":"34829","language":[{"iso":"eng"}],"article_type":"original","keyword":["regularity of Lie groups","differentiability of the evolution map"],"type":"journal_article","publication":"Forum Mathematicum","status":"public","date_created":"2022-12-22T09:38:08Z","author":[{"first_name":"Maximilian","full_name":"Hanusch, Maximilian","id":"30905","last_name":"Hanusch"}],"volume":31,"date_updated":"2023-01-09T18:07:13Z","publisher":"Walter de Gruyter GmbH","doi":"10.1515/forum-2018-0310","title":"Differentiability of the evolution map and Mackey continuity","issue":"5","publication_status":"published","publication_identifier":{"issn":["1435-5337","0933-7741"]},"citation":{"mla":"Hanusch, Maximilian. “Differentiability of the Evolution Map and Mackey Continuity.” <i>Forum Mathematicum</i>, vol. 31, no. 5, Walter de Gruyter GmbH, 2019, pp. 1139–77, doi:<a href=\"https://doi.org/10.1515/forum-2018-0310\">10.1515/forum-2018-0310</a>.","short":"M. Hanusch, Forum Mathematicum 31 (2019) 1139–1177.","bibtex":"@article{Hanusch_2019, title={Differentiability of the evolution map and Mackey continuity}, volume={31}, DOI={<a href=\"https://doi.org/10.1515/forum-2018-0310\">10.1515/forum-2018-0310</a>}, number={5}, journal={Forum Mathematicum}, publisher={Walter de Gruyter GmbH}, author={Hanusch, Maximilian}, year={2019}, pages={1139–1177} }","apa":"Hanusch, M. (2019). Differentiability of the evolution map and Mackey continuity. <i>Forum Mathematicum</i>, <i>31</i>(5), 1139–1177. <a href=\"https://doi.org/10.1515/forum-2018-0310\">https://doi.org/10.1515/forum-2018-0310</a>","ama":"Hanusch M. Differentiability of the evolution map and Mackey continuity. <i>Forum Mathematicum</i>. 2019;31(5):1139-1177. doi:<a href=\"https://doi.org/10.1515/forum-2018-0310\">10.1515/forum-2018-0310</a>","chicago":"Hanusch, Maximilian. “Differentiability of the Evolution Map and Mackey Continuity.” <i>Forum Mathematicum</i> 31, no. 5 (2019): 1139–77. <a href=\"https://doi.org/10.1515/forum-2018-0310\">https://doi.org/10.1515/forum-2018-0310</a>.","ieee":"M. Hanusch, “Differentiability of the evolution map and Mackey continuity,” <i>Forum Mathematicum</i>, vol. 31, no. 5, pp. 1139–1177, 2019, doi: <a href=\"https://doi.org/10.1515/forum-2018-0310\">10.1515/forum-2018-0310</a>."},"intvolume":"        31","page":"1139-1177","year":"2019"},{"type":"journal_article","publication":"Forum Mathematicum","status":"public","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>Let <jats:inline-formula id=\"j_forum-2018-0150_ineq_9999_w2aab3b7c12b1b6b1aab1c17b1b1Aa\">\r\n                     <jats:alternatives>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mrow>\r\n                              <m:mi>G</m:mi>\r\n                              <m:mo>/</m:mo>\r\n                              <m:mi>H</m:mi>\r\n                           </m:mrow>\r\n                        </m:math>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2018-0150_eq_0103.png\" />\r\n                        <jats:tex-math>{G/H}</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula> be a reductive symmetric space of split rank one and let <jats:italic>K</jats:italic> be a maximal compact subgroup of <jats:italic>G</jats:italic>. In a previous article the first two authors introduced a notion of cusp forms for <jats:inline-formula id=\"j_forum-2018-0150_ineq_9998_w2aab3b7c12b1b6b1aab1c17b1b7Aa\">\r\n                     <jats:alternatives>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mrow>\r\n                              <m:mi>G</m:mi>\r\n                              <m:mo>/</m:mo>\r\n                              <m:mi>H</m:mi>\r\n                           </m:mrow>\r\n                        </m:math>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2018-0150_eq_0103.png\" />\r\n                        <jats:tex-math>{G/H}</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula>. We show that the space of cusp forms coincides with the closure of the space of <jats:italic>K</jats:italic>-finite generalized matrix coefficients of discrete series representations if and only if there exist no <jats:italic>K</jats:italic>-spherical discrete series representations. Moreover, we prove that every <jats:italic>K</jats:italic>-spherical discrete series representation occurs with multiplicity one in the Plancherel decomposition of <jats:inline-formula id=\"j_forum-2018-0150_ineq_9997_w2aab3b7c12b1b6b1aab1c17b1c15Aa\">\r\n                     <jats:alternatives>\r\n                        <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\r\n                           <m:mrow>\r\n                              <m:mi>G</m:mi>\r\n                              <m:mo>/</m:mo>\r\n                              <m:mi>H</m:mi>\r\n                           </m:mrow>\r\n                        </m:math>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2018-0150_eq_0103.png\" />\r\n                        <jats:tex-math>{G/H}</jats:tex-math>\r\n                     </jats:alternatives>\r\n                  </jats:inline-formula>.</jats:p>"}],"user_id":"52730","_id":"64277","language":[{"iso":"eng"}],"issue":"2","publication_status":"published","publication_identifier":{"issn":["1435-5337","0933-7741"]},"citation":{"short":"E.P. van den Ban, J.J. Kuit, H. Schlichtkrull, Forum Mathematicum 31 (2018) 341–349.","bibtex":"@article{van den Ban_Kuit_Schlichtkrull_2018, title={K-invariant cusp forms for reductive symmetric spaces of split rank one}, volume={31}, DOI={<a href=\"https://doi.org/10.1515/forum-2018-0150\">10.1515/forum-2018-0150</a>}, number={2}, journal={Forum Mathematicum}, publisher={Walter de Gruyter GmbH}, author={van den Ban, Erik P. and Kuit, Job J. and Schlichtkrull, Henrik}, year={2018}, pages={341–349} }","mla":"van den Ban, Erik P., et al. “K-Invariant Cusp Forms for Reductive Symmetric Spaces of Split Rank One.” <i>Forum Mathematicum</i>, vol. 31, no. 2, Walter de Gruyter GmbH, 2018, pp. 341–49, doi:<a href=\"https://doi.org/10.1515/forum-2018-0150\">10.1515/forum-2018-0150</a>.","ama":"van den Ban EP, Kuit JJ, Schlichtkrull H. K-invariant cusp forms for reductive symmetric spaces of split rank one. <i>Forum Mathematicum</i>. 2018;31(2):341-349. doi:<a href=\"https://doi.org/10.1515/forum-2018-0150\">10.1515/forum-2018-0150</a>","apa":"van den Ban, E. P., Kuit, J. J., &#38; Schlichtkrull, H. (2018). K-invariant cusp forms for reductive symmetric spaces of split rank one. <i>Forum Mathematicum</i>, <i>31</i>(2), 341–349. <a href=\"https://doi.org/10.1515/forum-2018-0150\">https://doi.org/10.1515/forum-2018-0150</a>","chicago":"Ban, Erik P. van den, Job J. Kuit, and Henrik Schlichtkrull. “K-Invariant Cusp Forms for Reductive Symmetric Spaces of Split Rank One.” <i>Forum Mathematicum</i> 31, no. 2 (2018): 341–49. <a href=\"https://doi.org/10.1515/forum-2018-0150\">https://doi.org/10.1515/forum-2018-0150</a>.","ieee":"E. P. van den Ban, J. J. Kuit, and H. Schlichtkrull, “K-invariant cusp forms for reductive symmetric spaces of split rank one,” <i>Forum Mathematicum</i>, vol. 31, no. 2, pp. 341–349, 2018, doi: <a href=\"https://doi.org/10.1515/forum-2018-0150\">10.1515/forum-2018-0150</a>."},"page":"341-349","intvolume":"        31","year":"2018","date_created":"2026-02-19T13:28:57Z","author":[{"full_name":"van den Ban, Erik P.","last_name":"van den Ban","first_name":"Erik P."},{"full_name":"Kuit, Job J.","last_name":"Kuit","first_name":"Job J."},{"first_name":"Henrik","full_name":"Schlichtkrull, Henrik","last_name":"Schlichtkrull"}],"volume":31,"date_updated":"2026-02-19T13:29:20Z","publisher":"Walter de Gruyter GmbH","doi":"10.1515/forum-2018-0150","title":"K-invariant cusp forms for reductive symmetric spaces of split rank one"}]