TY - JOUR
TI - Cuspidal discrete series for projective hyperbolic spaces
LA - eng
PB - American Mathematical Society
AU - Andersen, Nils Byrial
AU - Flensted-Jensen, Mogens
A2 - Quinto, Eric Todd, Gonzalez, Fulton, Christensen, Jens Gerlach
JF - Contemporary Mathematics
VL - 598
SP - 59
EP - 75
PY - 2013
SN - 02714132, 10983627
SN - 9780821887387, 9781470410261
AB - Abstract. We have in [1] proposed a definition of cusp forms on semisimple symmetric spaces G/H, involving the notion of a Radon transform and a related Abel transform. For the real non-Riemannian hyperbolic spaces, we showed that there exists an infinite number of cuspidal discrete series, and at most finitely many non-cuspidal discrete series, including in particular the spherical discrete series. For the projective spaces, the spherical discrete series are the only non-cuspidal discrete series. Below, we extend these results to the other hyperbolic spaces, and we also study the question of when the Abel transform of a Schwartz function is again a Schwartz function.
DO - 10.1090/conm/598/11986
ER -