Studies on holomorphic mappings on the unit ball in an infinite dimensional space

无限维空间中单位球的全纯映射研究

• 批准号: 15540193
• 负责人: HONDA Tatsuhiro
• 金额: $ 1.02万
• 依托单位: Hiroshima Institute of Technology (2005)Ariake National College of Technology (2003-2004)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540193/
• 关键词: convex mapping; Loewner chain; parametric representation; spirallike mapping; starlike mapping; transition mapping; univalent holomorphic mapping; univalent holomorphic mapping; 増大定理; 媒介変数表現; ハルナック; starlike; 双正則

(1)We consider some equalities of the Hamack type and its applications for holomorphic mappings on some infinite dimensional domain.(2)Let E be a complex Banach space with an unconditional Schauder bass. Let D be a pseudoconvex domain in E and let V be a closed complex submanifold in E. We assume that the dimension of V is finite or the coon of V for E is finite. We denote by O the sheaf of germs of all holomorphic fuctions on D. Then we show that H^P(D＼V,O)=O for 1 □ p<codim_E V -1. Especially, if the dimension of V is finite and the dimension of E is infinite, then H^P(D＼V,O)=0 for p≧1 and D＼V is not pseudoconvex.By using this insult, we show that H^P(P(E),O) = 0 for 1 □ p<dim E -1, where P(E) is the complex projective space induced from E.(3)Let B be the unit ball in C^n with respect to an arbitrary norm and let f(z,t) be a g-Loewner chain such that e^<-t>f(z,t)-z has a zero of order k+1 at z=0. We obtain growth and covering theorems for f(・,0).Moreover, we consider coefficient bounds and examples of mappings in S_<g,k+1>^0(B).(4)Let B be the unit ball of a complex Banach space with respect to the noem. We obtain growth and covering theorems for some holomorphic mapping with parametric representaion, and consider various examples.

（1）我们在某些无限的尺寸上考虑了带有无主管的schauder bass上的holomorthics映射。有限。 p（d \ v，o）= 0对于p≧1，d \ v不是pseudoconvex。通过使用这种侮辱，我们证明h^p（p（e），o）= 0 for从E.（3）让B相对于任意规范，在C^n中为单位球，让F（z，t）为G-loewner链，使得e^<-t> f（z，z，z， z，z，t）-z在z z = 0处的k+1阶的零为零。我们获得了f（・，0）的生长和覆盖物。在s_ <g，k+1> ^0（b）中以外。 （4）让我们相对于NOEM的复杂的Banach空间。

项目成果

Holomorphic Mappings on Some Infinite Dimensional Domain

某个无限维域上的全纯映射

• 发表时间: 2004
• 期刊: Research Reports of the Ariake College of Technology 40
• 作者: M.Hirokawa;F.Hiroshima;H.Spohn;Tatsuhiro HONDA;Tatsuhiro HONDA
• 通讯作者: Tatsuhiro HONDA

Holomorphic mappings into some domain in a complex normed space

复杂赋范空间中某些域的全纯映射

• 发表时间: 2004
• 期刊: Journal of the Korean Mathematical Society 41-1
• 作者: Hirokawa;F.Hiroshima;H.Spohn;Tatsuhiro Honda
• 通讯作者: Tatsuhiro Honda

The Frenkel's lemma in Banach spaces and its applications

Banach空间中的Frenkel引理及其应用

• 发表时间: 2004
• 期刊: Far East Journal of Mathematical Sciences 14-1
• 作者: T.Honda;M.Miyagi;M.Nishihara;S.Ohgai;M.Yoshida
• 通讯作者: M.Yoshida

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

Holomorphic Mappings with Parametric Representation

具有参数表示的全纯映射

• 发表时间: 2005
• 期刊: Research Reports of the Ariake College of Technology 41
• 作者: M.Hirokawa;F.Hiroshima;H.Spohn;Tatsuhiro HONDA
• 通讯作者: Tatsuhiro HONDA