CUSPIDAL DISCRETE SERIES FOR PROJECTIVE HYPERBOLIC SPACES
CUSPIDAL DISCRETE SERIES FOR PROJECTIVE HYPERBOLIC SPACES
复制标题
射影双曲空间的尖端离散级数
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
M. Flensted
中科院分区：
文献类型：
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作者：
N. B. Andersen;M. Flensted
我们在(1)中提出了半单对称空间G/H上的尖点形式的定义，涉及到Radon变换和相关的Abel变换的概念。对于实非黎曼双曲空间，我们证明了存在无穷多个尖点离散级数，至多存在有限个非尖点离散级数，特别是球面离散级数。对于射影空间，球面离散级数是唯一的非尖点离散级数。下面，我们将这些结果推广到其他双曲空间，并研究了Schwartz函数的Abel变换何时又是Schwartz函数的问题。
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.