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

共 45 条

[1] The Heat Kernel and Green Functions of Sub-Laplacians on the Quaternion Heisenberg Group
Jingzhi Tie
M. W. Wong
Journal of Geometric Analysis, 2009, 19
[2] ON GREEN FUNCTIONS FOR DIRICHELET SUB-LAPLACIANS ON A QUATERNION HEISENBERG GROUP
Sabitbek, Bolys
Suragan, Durvudkhan
MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2018, 13 (04)
[3] HEAT KERNELS AND GREEN FUNCTIONS OF SUB-LAPLACIANS ON HEISENBERG GROUPS WITH MULTI-DIMENSIONAL
Molahajloo, Shahla
Wong, M. W.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2018, 13 (04)
[4] Green's Identities for (p, q)-Sub-Laplacians on the Heisenberg Group and Their Applications
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Suragan, Durvudkhan
COMPLEX ANALYSIS AND OPERATOR THEORY, 2022, 16 (03)
[5] Green’s Identities for (p, q)-Sub-Laplacians on the Heisenberg Group and Their Applications
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Complex Analysis and Operator Theory, 2022, 16
[6] Local solvability for positive combinations of generalized sub-Laplacians on the Heisenberg group
Müller, D
Zhang, ZQ
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (10) : 3101 - 3107
[7] Trace of heat kernel,spectral zeta function and isospectral problem for sub-laplacians
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Science China Mathematics, 2009, (12) : 2570 - 2589
[8] On Green functions for Dirichlet sub-Laplacians on H-type groups
Garofalo, Nicola
Ruzhansky, Michael
Suragan, Durvudkhan
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 452 (02) : 896 - 905
[9] Trace of heat kernel, spectral zeta function and isospectral problem for sub-laplacians
Der-Chen Chang
Sai-Kee Yeung
Science in China Series A: Mathematics, 2009, 52 : 2570 - 2589
[10] Trace of heat kernel, spectral zeta function and isospectral problem for sub-laplacians
Chang Der-Chen
Yeung Sai-Kee
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2009, 52 (12): : 2570 - 2589

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