| 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)
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| Research Abstract |
(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.
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