An application of hypergeometric shift operators to the chi-spherical Fourier transform
An application of hypergeometric shift operators to the chi-spherical Fourier transform
复制标题
超几何移位算子在卡球傅立叶变换中的应用
DOI：
10.1090/conm/650/13043
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
G. Ólafsson
中科院分区：
文献类型：
--
作者：
Vivian M. Ho;G. Ólafsson
研究了$BC_n$型根和一些负多重型的Heckman-Opdam超几何函数上的超几何移位算子的作用。这些超几何函数连接到厄米对称空间$U/K$上的$\chi$球面函数，其中$\chi$是$K$的非平凡特征。我们将移位算子应用于超几何函数，将负的多重性变为正的多重性。这允许我们使用与正多重相关的超几何函数的许多众所周知的结果。特别地，我们使用这种技术来实现$\chi$-球面函数的指数估计。其动机来自于厄米对称空间上的线束的Paley-Wiener型定理。
We study the action of hypergeometric shift operators on the Heckman-Opdam hypergeometric functions associated with the $BC_n$ type root system and some negative multiplicities. Those hypergeometric functions are connected to the $\chi$-spherical functions on Hermitian symmetric spaces $U/K$ where $\chi$ is a nontrivial character of $K$. We apply shift operators to the hypergeometric functions to move negative multiplicities to positive ones. This allows us to use many well-known results of the hypergeometric functions associated with positive multiplicities. In particular, we use this technique to achieve exponential estimates for the $\chi$-spherical functions. The motive comes from the Paley-Wiener type theorem on line bundles over Hermitian symmetric spaces.