| Asymptotics for Certain Harmonic Functions and the Martin Compactification on the Quaternionic Heisenberg Group |
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| 作者姓名： | Jing Wen LUAN Fu Liu ZHU |
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| 作者单位： | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. of China |
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| 基金项目： | Supported by the National Natural Science Foundation of China, Grant 10261002 |
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| 摘 要： |
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| 关 键 词： | 渐进线 Heisenberg群 谐波函数 逼近估计 Martin边界 |
| 收稿时间： | 2003-06-18 |
| 修稿时间： | 2003-06-182004-07-19 |
Asymptotics for Certain Harmonic Functions and the Martin Compactificationon on the Quaternionic Heisenberg Group |
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| Jing Wen LUAN Fu Liu ZHU.Asymptotics for Certain Harmonic Functions and the Martin Compactification on the Quaternionic Heisenberg Group[J].Acta Mathematica Sinica,2005,21(6):1295-1308. |
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| Authors: | Jing Wen Luan Fu Liu Zhu |
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| Institution: | (1) School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. of China |
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| Abstract: | In this paper, we make the asymptotic estimates of the heat kernel for the quaternionic Heisenberg group in various cases. We also use these results to deduce the asymptotic estimates of certain harmonic functions on the quaternionic Heisenberg group. Moreover a Martin compactification of the quaternionic Heisenberg group is constructed, and we prove that the Martin boundary of this group is homeomorphic to the unit ball in the quaternionic field. |
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| Keywords: | Quaternionic Heisenberg group Asymptotic estimate Heat kernel Martin boundary |
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