NA群上调和函数(英文)  

HARMONIC FUNCTIONS ON NA GROUPS

作　　者：王伟沧[1,2] 

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072 [2]武汉理工大学理学院,湖北武汉430063

出　　处：《数学杂志》2012年第5期803-808,共6页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(10871152)

摘　　要：本文研究了非对称调和流形上满足平均值性质的可积函数与卷积方程的解之关系.利用Naten,Weit在秩为一的对称空间上使用的谱综合方法,获得了NA群上卷积方程的可积函数解必是调和函数,这推广了Ahern,Flores和Rudin在欧氏空间,与Koranyi在双曲空间上得到的类似结果.We study the relation of the functions satisfying mean value property between solutions of convolution equations on no-symmetric harmonic manifolds. Through the spectral synthesis method used by Naten and Weit, we obtain the conclusion that the integrable solutions of convolution equations are harmonic on NA groups, which generalize the result showed by Ahern, Flores and Rudin in Euclid spaces and by Koranyi in the hyperbolicspaces.

关 键 词：NA群 球面变换 调和函数 

分 类 号：O152.5[理学—数学]