与根系相关的heat equation的Segal-Bargmann变换
The Segal-Bargmann transform for the heat equation associated with root systems
摘要：
研究了根系上重数函数所对应的热方程，其中相应的Laplace算子已由Heckman和Opdam定义.特别是，我们描述了图像的相关Segal-Bargmann变换作为一个空间的全纯函数。在重数函数对应于非紧型黎曼对称空间G/K的情况下，我们得到了G/K上K不变L^2函数空间在G/K上热方程的Segal-Bargmann变换下的象的描述，从而推广和改进了B.大厅为复杂类型的空间。
英文摘要：
We study the heat equation associated to a multiplicity function on a root system, where the corresponding Laplace operator has been defined by Heckman and Opdam. In particular, we describe the image of the associated Segal-Bargmann transform as a space of holomorphic functions. In the case where the multiplicity function corresponds to a Riemannian symmetric space G/K of noncompact type, we obtain a description of the image of the space of K-invariant L^2-function on G/K under the Segal-Bargmann transform associated to the heat equation on G/K, thus generalizing (and reproving) a result of B. Hall for spaces of complex type.
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