A Note on the Heat Kernel for the Rescaled Harmonic Oscillator from Two Step Nilpotent Lie Groups  

作　　者：Zhi Peng YANG 

机构地区：[1]Department of Mathematics,Yunnan Normal University,Kunming 650500,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第9期1597-1611,共15页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos.12101546,11771385)。

摘　　要：In this note,we use Schr?dinger representations and the Fourier transform on two step nilpotent Lie groups to compute the explicit formula of the sub-Laplacian operator and its symbol,which is associated with the rescaled harmonic oscillator.Then we can give an explicit formula for the heat kernel of the rescaled harmonic oscillator for the singularity at the origin.Our results are useful for the general two step nilpotent Lie groups,including the Heisenberg group and H-type group.

关 键 词：SUB-LAPLACIAN heat kernel nilpotent Lie groups 

分 类 号：O152.5[理学—数学]