CAJ | 학술논문

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.
본문연구료비대칭조화류형상만족평균치성질적가적함수여권적방정적해지관계.이용Naten,Weit재질위일적대칭공간상사용적보종합방법,획득료NA군상권적방정적가적함수해필시조화함수,저추엄료Ahern,Flores화Rudin재구씨공간,여Koranyi재쌍곡공간상득도적유사결과.
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.