Cuspidal discrete series for projective hyperbolic spaces
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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.
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.
Originalsprog | Engelsk |
---|---|
Bogserie | Contemporary Mathematics |
Vol/bind | 598 |
Sider (fra-til) | 59-75 |
ISSN | 0271-4132 |
Status | Udgivet - 2013 |
ID: 95314149