Application of Nilpotent Approximation and the Orbit Method to the Search of the Diagonal Asymptotics of Sub-Riemannian Heat Kernels

Сибирский математический журнал

article

M. V. Kuznetsov¹ 

[1] Sobolev Institute of Mathematics

关键词: nilpotent Lie group;    sub-Laplacian;    noncommutative harmonic analysis;    representation theory;    orbit method;   

DOI  :  10.1134/S0037446619060132

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

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.

【 授权许可】

CC BY