海森堡次拉普拉斯算子和格鲁辛算子的热核渐近展开式。
Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator.
作者信息
Chang Der-Chen, Li Yutian
机构信息
Department of Mathematics and Department of Computer Sciences , Georgetown University , Washington, DC 20057, USA ; Department of Mathematics , Fu Jen Catholic University , Taipei 242, Taiwan, Republic of China.
Department of Mathematics, and Institute for Computational and Theoretical Studies , Hong Kong Baptist University , Kowloon, Hong Kong.
出版信息
Proc Math Phys Eng Sci. 2015 Mar 8;471(2175):20140943. doi: 10.1098/rspa.2014.0943.
The sub-Laplacian on the Heisenberg group and the Grushin operator are typical examples of sub-elliptic operators. Their heat kernels are both given in the form of Laplace-type integrals. By using Laplace's method, the method of stationary phase and the method of steepest descent, we derive the small-time asymptotic expansions for these heat kernels, which are related to the geodesic structure of the induced geometries.
海森堡群上的次拉普拉斯算子和格鲁辛算子是次椭圆算子的典型例子。它们的热核都以拉普拉斯型积分的形式给出。通过使用拉普拉斯方法、驻相法和最速下降法，我们推导出了这些热核的小时间渐近展开式，这些展开式与诱导几何的测地线结构有关。
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