C^n中单位球上推广的Roper-Suffridge算子与Loewner链  

Generalized Roper-Suffridge Extension Operator on the Unit Ball in C^n and Loewner Chains

作　　者：崔艳艳[1] 王朝君[1] 

机构地区：[1]周口师范学院数学与信息科学系,中国周口466001

出　　处：《湖南师范大学自然科学学报》2013年第5期7-11,共5页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(1271359;U1204618);河南省教育厅自然科学基金资助项目(2011B110034);河南省科技厅软科学资助项目(102400450003)

摘　　要：在Cn中的单位球上进一步推广了Roper-Suffridge算子,并讨论推广后的算子保持双全纯映照子族的性质,证明在一定条件下,推广后的Roper-Suffridge算子在Cn中的单位球Bn上能嵌入Loewner链,进而从Loewner链的角度出发证明推广后的算子在一定条件下保持α次殆β型螺形性,从而得出推广后的Roper-Suffridge算子在一定条件下在Bn上保持β型螺形性,α次殆星形性及星形性.The Roper-Suffridge extension operator is ulteriorly generalized on the unit ball in C^n, and it is discussed that the generalized operator preserves some properties of subclasses of biholomorphic mappings. The fact that the generalized operator can be embeded in a Loewner chains under certain conditions on the unit ball in Cn is proved. And that the generalized operator preserves almost spirallikeness of typeβ and order a under certain conditions is proved from the point of view of Loewner chains, thereby the generalized operator can preserve spirallikeness of typeβ, almost starlikeness of order α and starlikeness under certain conditions on B^n.

关 键 词：α次殆β型螺形映照 Loewner链 ROPER-SUFFRIDGE算子 

分 类 号：O174.56[理学—数学]