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关于局部双全纯映射的推广的Roper-Suffridge算子
引用本文:刘小松,刘太顺.关于局部双全纯映射的推广的Roper-Suffridge算子[J].数学季刊,2003,18(3):221-229.
作者姓名:刘小松  刘太顺
作者单位:Department of Mathematics,University of Science and Technology of C hina,Hefei 230026,China
基金项目:Supportedbythe973plan(G19990 7510 5)
摘    要:§ 1. Introduction  LetUbetheunitdiskinCandBnbetheunitballinCn.In 1 995 ,RoperandSuffridgeintroducedanextensionoperator.ThisoperatorisdefinedforanormalizedlocallybiholomorphicfunctionfonUbyΦn(f) (z) =F(z) =(f(z1 ) ,f′(z1 )z′) ,z =(z1 ,z′)∈Bn,(1 .1 )wherez1 ∈U ,z′=(z2 ,… ,zn)∈Cn- 1 ,andthebranchofthesquarerootischosensuchthatf′(0 ) =1 .TheRoper Suffridgeextensionoperatorhasthefollowingimportantproperties:(a)IffisanormalizedconvexfunctiononU ,thenFisanormalizedconvexmappingon…

关 键 词:广义Roper-Suffridge扩张算子  局部双全纯映射  星形性  Reinhardt域  凸性  增长定理  畸变定理

The Generalized Roper-Suffridge Extension Operator for Locally Biholomorphic Mappings
LIU Xiao-song,LIU Tai-shun.The Generalized Roper-Suffridge Extension Operator for Locally Biholomorphic Mappings[J].Chinese Quarterly Journal of Mathematics,2003,18(3):221-229.
Authors:LIU Xiao-song  LIU Tai-shun
Institution:DepartmentofMathematics,UniversityofScienceandTechnologyofChina,Hefei230026,China
Abstract:In this paper, we introduce the generalized Roper-Suffridge extension operator for locally bi-holomorphic mappings. It is shown that this operator preserves the starlikeness on some Reinhardt do-mains and does not preserve convexity for some cases. Meanwhile, the growth theorem and distortion theorem of the corresponding mappings are given.
Keywords:biholomorphic mappings  starlike mappings and convex  mappings  the generalized Roper-Suffridge extension operator
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