Asymptotics for Certain Harmonic Functions and the Martin Compactification on the Quaternionic Heisenberg Group  

作　　者：Jing Wen LUAN Fu Liu ZHU 

机构地区：[1]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. of China

出　　处：《Acta Mathematica Sinica,English Series》2005年第6期1295-1308,共14页数学学报（英文版）

基　　金：the National Natural Science Foundation of China Grant 10261002

摘　　要：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.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.

关 键 词：Quaternionic Heisenberg group Asymptotic estimate Heat kernel Martin boundary 

分 类 号：O174.41[理学—数学]