For reductive symmetric spaces \r\n\r\n \r\n \r\n G\r\n \r\n /\r\n \r\n H\r\n \r\n G/H\r\n \r\n\r\n of split rank one we identify a class of minimal parabolic subgroups for which certain cuspidal integrals of Harish-Chandra–Schwartz functions are absolutely convergent. Using these integrals we introduce a notion of cusp forms and investigate its relation with representations of the discrete series for \r\n\r\n \r\n \r\n G\r\n \r\n /\r\n \r\n H\r\n \r\n G/H\r\n \r\n\r\n.
"}],"publication":"Representation Theory of the American Mathematical Society","type":"journal_article","language":[{"iso":"eng"}],"user_id":"52730","_id":"64279","page":"467-533","intvolume":" 21","citation":{"short":"E. van den Ban, J. Kuit, Representation Theory of the American Mathematical Society 21 (2017) 467–533.","bibtex":"@article{van den Ban_Kuit_2017, title={Cusp forms for reductive symmetric spaces of split rank one}, volume={21}, DOI={10.1090/ert/507}, number={17}, journal={Representation Theory of the American Mathematical Society}, publisher={American Mathematical Society (AMS)}, author={van den Ban, Erik and Kuit, Job}, year={2017}, pages={467–533} }","mla":"van den Ban, Erik, and Job Kuit. “Cusp Forms for Reductive Symmetric Spaces of Split Rank One.” Representation Theory of the American Mathematical Society, vol. 21, no. 17, American Mathematical Society (AMS), 2017, pp. 467–533, doi:10.1090/ert/507.","apa":"van den Ban, E., & Kuit, J. (2017). Cusp forms for reductive symmetric spaces of split rank one. Representation Theory of the American Mathematical Society, 21(17), 467–533. https://doi.org/10.1090/ert/507","ama":"van den Ban E, Kuit J. Cusp forms for reductive symmetric spaces of split rank one. Representation Theory of the American Mathematical Society. 2017;21(17):467-533. doi:10.1090/ert/507","ieee":"E. van den Ban and J. Kuit, “Cusp forms for reductive symmetric spaces of split rank one,” Representation Theory of the American Mathematical Society, vol. 21, no. 17, pp. 467–533, 2017, doi: 10.1090/ert/507.","chicago":"Ban, Erik van den, and Job Kuit. “Cusp Forms for Reductive Symmetric Spaces of Split Rank One.” Representation Theory of the American Mathematical Society 21, no. 17 (2017): 467–533. https://doi.org/10.1090/ert/507."},"year":"2017","issue":"17","publication_identifier":{"issn":["1088-4165"]},"publication_status":"published","doi":"10.1090/ert/507","title":"Cusp forms for reductive symmetric spaces of split rank one","volume":21,"date_created":"2026-02-19T13:31:09Z","author":[{"first_name":"Erik","last_name":"van den Ban","full_name":"van den Ban, Erik"},{"first_name":"Job","full_name":"Kuit, Job","last_name":"Kuit"}],"date_updated":"2026-02-19T13:31:21Z","publisher":"American Mathematical Society (AMS)"}