{"volume":31,"author":[{"first_name":"Erik P.","last_name":"van den Ban","full_name":"van den Ban, Erik P."},{"first_name":"Job J.","full_name":"Kuit, Job J.","last_name":"Kuit"},{"first_name":"Henrik","last_name":"Schlichtkrull","full_name":"Schlichtkrull, Henrik"}],"date_created":"2026-02-19T13:28:57Z","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","issue":"2","publication_identifier":{"issn":["1435-5337","0933-7741"]},"publication_status":"published","page":"341-349","intvolume":" 31","citation":{"ieee":"E. P. van den Ban, J. J. Kuit, and H. Schlichtkrull, “K-invariant cusp forms for reductive symmetric spaces of split rank one,” Forum Mathematicum, vol. 31, no. 2, pp. 341–349, 2018, doi: 10.1515/forum-2018-0150.","chicago":"Ban, Erik P. van den, Job J. Kuit, and Henrik Schlichtkrull. “K-Invariant Cusp Forms for Reductive Symmetric Spaces of Split Rank One.” Forum Mathematicum 31, no. 2 (2018): 341–49. https://doi.org/10.1515/forum-2018-0150.","apa":"van den Ban, E. P., Kuit, J. J., & Schlichtkrull, H. (2018). K-invariant cusp forms for reductive symmetric spaces of split rank one. Forum Mathematicum, 31(2), 341–349. https://doi.org/10.1515/forum-2018-0150","ama":"van den Ban EP, Kuit JJ, Schlichtkrull H. K-invariant cusp forms for reductive symmetric spaces of split rank one. Forum Mathematicum. 2018;31(2):341-349. doi:10.1515/forum-2018-0150","short":"E.P. van den Ban, J.J. Kuit, H. Schlichtkrull, Forum Mathematicum 31 (2018) 341–349.","mla":"van den Ban, Erik P., et al. “K-Invariant Cusp Forms for Reductive Symmetric Spaces of Split Rank One.” Forum Mathematicum, vol. 31, no. 2, Walter de Gruyter GmbH, 2018, pp. 341–49, doi:10.1515/forum-2018-0150.","bibtex":"@article{van den Ban_Kuit_Schlichtkrull_2018, title={K-invariant cusp forms for reductive symmetric spaces of split rank one}, volume={31}, DOI={10.1515/forum-2018-0150}, 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} }"},"year":"2018","user_id":"52730","_id":"64277","language":[{"iso":"eng"}],"publication":"Forum Mathematicum","type":"journal_article","status":"public","abstract":[{"lang":"eng","text":"Abstract\r\n Let \r\n \r\n \r\n \r\n G\r\n /\r\n H\r\n \r\n \r\n \r\n {G/H}\r\n \r\n be a reductive symmetric space of split rank one and let K be a maximal compact subgroup of G. In a previous article the first two authors introduced a notion of cusp forms for \r\n \r\n \r\n \r\n G\r\n /\r\n H\r\n \r\n \r\n \r\n {G/H}\r\n \r\n . We show that the space of cusp forms coincides with the closure of the space of K-finite generalized matrix coefficients of discrete series representations if and only if there exist no K-spherical discrete series representations. Moreover, we prove that every K-spherical discrete series representation occurs with multiplicity one in the Plancherel decomposition of \r\n \r\n \r\n \r\n G\r\n /\r\n H\r\n \r\n \r\n \r\n {G/H}\r\n \r\n ."}]}