Product formulas for a two-parameter family of Heckman-Opdam hypergeometric functions of type BC
Product formulas for a two-parameter family of Heckman-Opdam hypergeometric functions of type BC
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BC 型 Heckman-Opdam 超几何函数二参数族的乘积公式
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Voit
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文献类型：
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作者：
M. Voit
本文给出了$B$的Weylchambers $C_q\subset \mathbb R^q$上的连续两参数BC型Heckman-Opdam超几何函数族的显式乘积公式.这些公式与$C_q\times\mathbb R$上的保概率卷积结构的连续单参数族有关。这些在$C_q\times\mathbb R$上的卷积是通过对称空间$U（p，q）/（U（p）\times SU（q））$的球面函数的乘积公式和在$C_q\times\mathbb T $上与环面$\mathbb T$相关的双陪集卷积构造的。我们将得到正积公式的限制参数集，而相关的卷积总是范数递减。本文给出了三个BC型Heckman-Opdam超几何函数级数的Rosler最近的正积公式以及秩q=1的Koornwinder和Trimeche的Jacobi函数的经典积公式.
In this paper we present explicit product formulas for a continuous two-parameter family of Heckman-Opdam hypergeometric functions of type BC on Weyl chambers $C_q\subset \mathbb R^q$ of type $B$. These formulas are related to continuous one-parameter families of probability-preserving convolution structures on $C_q\times\mathbb R$. These convolutions on $C_q\times\mathbb R$ are constructed via product formulas for the spherical functions of the symmetric spaces $U(p,q)/ (U(p)\times SU(q))$ and associated double coset convolutions on $C_q\times\mathbb T$ with the torus $\mathbb T$. We shall obtain positive product formulas for a restricted parameter set only, while the associated convolutions are always norm-decreasing. Our paper is related to recent positive product formulas of R\"osler for three series of Heckman-Opdam hypergeometric functions of type BC as well as to classical product formulas for Jacobi functions of Koornwinder and Trimeche for rank $q=1$.
影响因子：
1.7
作者：
Raetz, Andreas;Roeger, Matthias
通讯作者：
Roeger, Matthias