2006 Fiscal Year Final Research Report Summary
A study on the proper holomorphic mappings and univalent holomorphic mappings on the unit ball
| Project/Area Number |
17540183
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu Sangyo University |
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Principal Investigator |
HAMADA Hidetaka Kyushu Sangyo University, Faculty of Engineering, Professor, 工学部, 教授 (30198808)
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| Project Period (FY) |
2005 – 2006
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| Keywords | transition mapping / biholomorphic mapping / rational mapping / univalent holomorohic mapping / starlike mapping / convex mapping |
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| Research Abstract |
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.
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