双解析函数的性质

Properties of Bianalitic Function

研究了双解析函数非孤立零点的分布,映射性质以及孤立奇点分类方法.首先利用解析函数唯一性,证明了双解析函数非孤立零点不能超过1阶.求出了曲线弧为双解析函数零点弧的条件.然后利用几何函数论中的方法得到了双解析函数为单叶保向同胚映射的条件.最后定义了双解析函数孤立奇点并给出与解析函数相似的孤立奇点分类方法,所讨论的内容既有与解析函数相似的性质,也有极不相同的性质.

Some properties of bianalytic functions were discussed about distribution of the non-isolated zeros, mapping property and classification of the isolated singularity. The result which order of nonisolated zeros was not over first order was proved by using the unique theorem of analytic functions, and condition which an curve arc became an arc of zeros of bianalytic functions was obtained. According to the methods of Geometric function theory, the condition that bianalytic functions was a univalent sense preserving homeomorphism mapping was obtained. The isolated singularity of bianalytic functions was defined and its classification problem was discussed. The contents discussed were same as analytic functions, by the same time some special properties were studied.