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

被引：0
作者：
Zhi Peng Yang
机构：
[1] Yunnan Normal University,Department of Mathematics
来源：
Acta Mathematica Sinica, English Series | 2022年 / 38卷
关键词：
Sub-Laplacian; heat kernel; nilpotent Lie groups; 22E25; 43A75; 35A08;
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摘要：
In this note, we use Schrödinger 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.
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页码：1597 / 1611
页数：14
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