We propose a general scheme for the search of a fundamental solution to the hypoelliptic diffusion equation in a “sufficiently good” sub-Riemannian manifold and the small-time asymptotics for the solution, which includes the generalized Fourier transform and the orbit method closely related to it, as well as an application of the perturbative method to the nilpotent approximation, and Trotter’s formula.

中文翻译：

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幂零逼近和轨道方法在亚黎曼热核对角渐近搜索中的应用

我们提出了一个一般方案，用于在“足够好”的次黎曼流形中寻找次椭圆扩散方程的基本解以及该解的小时间渐近性，其中包括广义傅里叶变换和与之密切相关的轨道方法。它，以及微扰方法在幂等逼近中的应用以及Trotter公式。