2012/09/14 by Nils Byrial Andersen, Andersen, Nils Byrial, Mogens Flensted-Jensen +1
Mathematics · #Advanced Algebra and Geometry #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1209.3124
Revised version, to appear in Contemporary Mathematics, Amer. Math. Soc
openalex publication_date 2012/09/14 · arxiv created 2013/01/03 · arxiv updated 2013/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.