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两类正规化双全纯映照子族齐次展开式的精细估计
引用本文:刘小松,刘太顺.两类正规化双全纯映照子族齐次展开式的精细估计[J].数学学报,2007,50(2):393-400.
作者姓名:刘小松  刘太顺
作者单位:湛江师范学院数学与计算科学学院,湖州师范学院数学系 湛江 524048,湖州 313000
基金项目:国家自然科学基金(10571164),教育部博士点基金(20050358052),广东省自然科学基金(06301315),广东湛江师范学院博士专项研究资助项目(Z0420)
摘    要:本文考虑C~n中单位多圆柱上和一般复Banach空间中单位球上的正规化双全纯α(0■α<1)次的殆β(-π/2<β<π/2)型螺形映照以及α(0<α<1)次的β(-π/2<β<π/2)型螺形映照f(其中x=0是f(x)-x的k+1阶零点),研究了它们的构造,并得到其齐次展开式的精细估计.所得的结果推广了以前相应的结论.

关 键 词:k+1阶零点  α次的殆β型螺形映照  α次的β型螺形映照
文章编号:0583-1431(2007)02-0393-08
收稿时间:2005-9-8
修稿时间:2005-09-08

The Refined Estimation of Homogeneous Expansion for Two Subclasses of Normalized Biholomorphic Mappings
Xiao Song LIU ,Tai Shun LIU.The Refined Estimation of Homogeneous Expansion for Two Subclasses of Normalized Biholomorphic Mappings[J].Acta Mathematica Sinica,2007,50(2):393-400.
Authors:Xiao Song LIU  Tai Shun LIU
Institution:Xiao Song LIU School of Mathematics and Computation Science,Zhanjiang Normal University,Zhanjiang 524048,P.R.China Tai Shun LIU Department of Mathematics,Huzhou Teacher's College,Huzhou 313000,P.R.China
Abstract:In this paper,we consider a normalized biholomorphic almost spirallike map- ping of typeβ(-π/2<β<π/2) and order a (0■α<1) or a normalized biholomorphic spirallike mapping of typeβ(-π/2<β<π/2) and order a (0<α<1) f defined on the unit polydisk of C~n and the unit ball in a complex Banach space,where x=0 is a zero of order k+1 of f(x)-x.We investigate its construction,and the refined estimation of homogeneous expansion for f(x)is obtained.Our result extends the corresponding known conclusions.
Keywords:Zero of order k+1  almost spirallike mapping of typeβand orderα  spirallike mapping of typeβand orderα
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