The Heat Kernel and Green Functions of Sub-Laplacians on the Quaternion Heisenberg Group

被引：10

作者：

Tie, Jingzhi ^{[1
]}

Wong, M. W. ^{[2
]}

机构：

[1] Univ Georgia, Dept Math, Athens, GA 30602 USA

[2] York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2009年 / 19卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Quaternion Heisengerg group; Sub-Laplacian; Heat kernel and fundamental solution; 35H20; 42B30; SUBELLIPTIC OPERATORS;

D O I：

10.1007/s12220-008-9038-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the quaternion Heisenberg group and show that it is a special case of the model step two nilpotent Lie group studied by Beals, Gaveau and Greiner. Using the heat kernel, we give formulas for Green functions of sub-Laplacians on the quaternion Heisenberg group.

引用

页码：191 / 210

页数：20

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