一类Roper——Suffridge算子的偏差定理  

Deviation Theorems of a Class of Roper-Suffridge Operators

作　　者：赵娜 

机构地区：[1]郑州工商学院

出　　处：《哈尔滨师范大学自然科学学报》2016年第6期11-15,25,共6页Natural Science Journal of Harbin Normal University

摘　　要：双全纯映照的系数估计和偏差定理是多复变函数论的重要组成部分,而Roper-Suffridge算子在由单复变数的全纯函数构造多复变数的双全纯映照中起着至关重要的作用.在多复变数的背景之下,以一类特殊的在Cn中的单位球Bn上保持星形性质的算子F(z)为研究对象,从单位圆盘上的星形函数入手来研究这类算子在n=2的偏差定理.并且验证了在n=1时是可以回到一维单复变中星形函数的偏差定理的情况.The coefficient estimates and. deviation theorems of biholomorphic mappings is an important part of complex function theory, which plays a vital role in the Roper - Suffridge operator by holomorphic functions of one complex variable structure of several complex variables. In this paper, under Biholomorphic Mappings in several complex variables in the background, a kind of special the unit ball on the operator keeping star property as the research object, the deviation theorem is studied for the class of operators in the starting from the star function on the unit disk. And back in one dimensional deviation theorems of starlike functions of complex situations is verified.

关 键 词：偏差定理 推广的Roper-Suffridge算子 星形映照 

分 类 号：O174.5[理学—数学]