Cuspidal discrete series for projective hyperbolic spaces
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Cuspidal discrete series for projective hyperbolic spaces. / Andersen, Nils Byrial; Flensted-Jensen, Mogens.
I: Contemporary Mathematics, Bind 598, 2013, s. 59-75.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Cuspidal discrete series for projective hyperbolic spaces
AU - Andersen, Nils Byrial
AU - Flensted-Jensen, Mogens
PY - 2013
Y1 - 2013
N2 - 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.
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.
M3 - Journal article
VL - 598
SP - 59
EP - 75
JO - Contemporary Mathematics
JF - Contemporary Mathematics
SN - 0271-4132
ER -
ID: 95314149