A study on the proper holomorphic mappings and univalent holomorphic mappings on the unit ball

单位球上真全纯映射和一价全纯映射的研究

• 批准号: 17540183
• 负责人: HAMADA Hidetaka
• 金额: $ 0.7万
• 依托单位: Kyushu Sangyo University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17540183/
• 关键词: transition mapping; biholomorphic mapping; rational mapping; univalent holomorohic mapping; starlike mapping; convex mapping; 螺旋型写像; 星型写像

1. We give a growth theorem and coefficient estimates for univalent holomorphic mappings which have parametric representation and we also give many examples.2. We obtain certain results related to radius of starlikeness, convexity, parametric representation and Bloch radius for some classes of holomorphic mappings on the unit ball B^n in C^n.3. Let B be the unit ball in C^n with respect to an arbitrary norm on C^n. We give a necessary and sufficient condition that a Loewner chain f(z, t), such that {e^<-t>f(z, t)},t>0 is a normal family on B, is k-fold symmetrical.4. We obtain certain necessary and sufficient conditions for a mapping to be a convex subordination chain and we give various examples of convex subordination chains on the Euclidean unit ball in C^n.5. We give starlike criteria for a class of rational mappings on the open unit ball of a complex Banach space. We also give a sufficient condition for these mappings to be convex when they are defined in Hilbert spaces.

1.给出了具有参数表示的单叶全纯映射的增长定理和系数估计，并给出了例子.得到了C ^n中单位球B^n上的几类全纯映射的星形半径、凸性、参数表示和Bloch半径等有关结果.设B是C^n中关于C^n上任意范数的单位球。我们给出了一个Loewner链f（z，t），使得{e^<-t>f（z，t）}，t&gt;0是B上的正规族，f（z，t）是k重代数的充要条件.我们得到了一个映射是凸从属链的充要条件，并给出了Cn中欧氏单位球上凸从属链的各种例子。给出了复Banach空间开单位球上一类有理映射的星形判别准则。当这些映射定义在Hilbert空间中时，我们也给出了它们是凸映射的一个充分条件。

项目成果

Starlike and Convex Rational Mappings on Infinite Dimensional Domains

无限维域上的星状和凸有理映射

• 发表时间: 2009
• 期刊: Mathematische Nachrichten 282, No.2
• 作者: Cho-Ho Chu;H.Hamada;本田竜広;G.Kohr
• 通讯作者: G.Kohr

Convex subordination chains in several complex variables

多个复杂变量中的凸从属链

• 发表时间: 2009
• 期刊: Canad.J.Math. 61
• 作者: I.Graham;H.Hamada;G.Kohr;J.A.Pfaltzgraff
• 通讯作者: J.A.Pfaltzgraff

Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation

• DOI: 10.1016/j.jmaa.2005.08.002
• 发表时间: 2006-05
• 期刊: Journal of Mathematical Analysis and Applications
• 影响因子: 1.3
• 作者: H. Hamada;Tatsuhiro Honda;G. Kohr

Radius problems for holomorphic mappings on the unit ball in C^n

C^n 中单位球上的全纯映射的半径问题

• 发表时间: 2006
• 期刊: Math. Nachr. 279
• 作者: I. Graham;H. Hamada and G. Kohr
• 通讯作者: H. Hamada and G. Kohr

k-fold symmetrical mappings and Loewner chains

k 重对称映射和 Loewner 链

• 发表时间: 2007
• 期刊: Demonstratio Mathematica 40
• 作者: H.Hamada;T.Honda and G.Kohr
• 通讯作者: T.Honda and G.Kohr