中文摘要：

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.

英文摘要：

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.