论文标题
Dunkl-Laplace Transform和MacDonald的超几何系列
The Dunkl-Laplace transform and Macdonald's hypergeometric series
论文作者
论文摘要
我们继续一个程序，从对称锥的分析到类型A的根系的DUNKL设置，尤其是我们证明了A型A型heckman-Opdam高几乎测定功能的dunkl laplace转换身份，更广泛地证明了相关的Cherednik kernel。这是通过从拉普拉斯变换身份的分析延续来实现的，用于对称案例的非对称插孔多项式，这是MacDonald（2013）未发表的手稿中的关键猜想。我们对杰克多项式的证明是基于dunkl操作员技术和诺普和萨希的升高操作员。此外，我们使用这些结果来建立Laplace在高温序列之间在插孔多项式方面的转化身份。最后，我们以Dunkl-Laplace变换的后旁边反转公式结束。
We continue a program generalizing classical results from the analysis on symmetric cones to the Dunkl setting for root systems of type A. In particular, we prove a Dunkl-Laplace transform identity for Heckman-Opdam hypergeometric functions of type A and more generally, for the associated Cherednik kernel. This is achieved by analytic continuation from a Laplace transform identity for non-symmetric Jack polynomials which was stated, for the symmetric case, as a key conjecture in an unpublished manuscript of Macdonald (2013). Our proof for the Jack polynomials is based on Dunkl operator techniques and the raising operator of Knop and Sahi. Moreover, we use these results to establish Laplace transform identities between hypergeometric series in terms of Jack polynomials. Finally, we conclude with a Post-Widder inversion formula for the Dunkl-Laplace transform.
