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

基本信息

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

项目摘要

(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）我们考虑了Hamack类型的某些平等性及其在某些无限尺寸域上用于全体形态映射的应用。（2）让E成为一个复杂的Banach空间，具有无条件的Schauder低音。令D为E中的伪共元域，让V为E中的一个封闭的复杂子手机。我们假设V的尺寸是有限的，或者v的Coon for E的COON是有限的。我们用D的o表示D。特别是，如果V的尺寸是有限的并且E的尺寸是无限的，则h^p（d \ v，o）= 0对于p≧1和d \ v不是伪convex。通过使用这种侮辱，我们表明h^p（p（e），o），o）对于1□p <e -e -e -e -e -e -e -e -e^be（e）的空间（e -e）均为c py（e -e）。相对于任意规范，让f（z，t）为G-loewner链，使得e^<-t> f（z，t）-z在z = 0时具有k+1的均值为零。我们获得了F（・，0）的生长并覆盖定理。此外，我们考虑了S_ <G，K+1>^0（B）中映射的系数和示例。（4）让B为复杂的Banach空间相对于NOEM的单位球。我们获得了具有参数表示的一些全体形态映射的生长和覆盖定理，并考虑了各种示例。