关于多元调和函数论中的唯一性定理

On the Uniqueness Theorems of Harmonic Functions of Several Variables

我们感兴趣的是将自变量为 2元时成立的某些较深刻的关于共轭调和函数系中的唯一性定理推广到 n元的情形 .当 n≤ 12时 ,它们不仅在上半空间 Rn+ 1+ 上成立 ,而且在更为一般的区域Ω Rn+ 1上也成立 .从而证明了 T.H.Wolff三大反例中的第一大反例是错误的 .

In this paper our particular interest will be to extend to n variables some of the deeper uniqueness theorems known to hold in the case of two variables. When n≤12, they hold not only in the half space R n+1 + , but also in more general region ΩR n+1 . So we prove that the first one of of the T.H.Wolff three counterexamples is wrong.