复反de Sitter纤维化的次椭圆热核的整表示
Integral representation of the subelliptic heat kernel on the complex anti-de Sitter fibration
摘要：
我们导出了复反de Sitter纤维化的次椭圆热核的整表示。我们的证明不同于王晶\cite{Wan}中的证明，因为它利用了D 'Alembertian和Laplacian作用于垂直变量的交换性，而不是利用实双曲空间的热半群的解析延拓.我们的方法还揭示了上述纤维化的子拉普拉斯算子和所谓的广义马斯拉普拉斯算子之间的联系，以及奇维实双曲空间所起的作用。
英文摘要：
We derive an integral representation for the subelliptic heat kernel of the complex anti-de Sitter fibration. Our proof is different from the one used in Jing Wang \cite{Wan} since it appeals to the commutativity of the D'Alembertian and of the Laplacian acting on the vertical variable rather than the analytic continuation of the heat semigroup of the real hyperbolic space. Our approach also sheds the light on the connection between the sub-Laplacian of the above fibration and the so-called generalized Maass Laplacian, and on the role played by the odd dimensional real hyperbolic space.
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