Studies on holomorphic mappings on the unit ball in an infinite dimensional space
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants|
|Research Institution||Hiroshima Institute of Technology(2005)|
Ariake National College of Technology(2003-2004)
HONDA Tatsuhiro Hiroshima Institute of Technology, Faculty of Engineering, Assistant Professor, 工学部, 助教授 (20241226)
|Project Period (FY)
2003 – 2005
Completed(Fiscal Year 2005)
|Budget Amount *help
¥1,600,000 (Direct Cost : ¥1,600,000)
Fiscal Year 2005 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 2004 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 2003 : ¥600,000 (Direct Cost : ¥600,000)
|Keywords||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.
Research Products (11results)