2000 Fiscal Year Final Research Report Summary
The extension of holomorphic functions on locally convex spaces
| Project/Area Number |
11640196
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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 | Fukuoka Institute of Technology |
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Principal Investigator |
NISHIHARA Masaru Faculty of Information Engineering, Fukuoka Institute of Technology, Professor, 情報工学部, 教授 (20112287)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIBATA Shinya Tokyo Institute of Technology, Graduate School of Information Science and Engineering, Associate Professor, 情報理工学部, 助教授 (80279299)
ITOKAWA Yoe Faculty of Information Engineering, Fukuoka Institute of Technology, Professor, 情報工学部, 教授 (90223205)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Entire functions / The topological tensor product / Nuclear spaces / Ricci curvature / Homology group / Hyperbolic-elliptic coupled systems / the discrete Bolzmann equation / ボルツマン方程式 |
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| Research Abstract |
Let E be a closed complex linear subspace of a complex locally convex space F.Then, Nishihara(HEAD INVESTIGATOR)investigated the problem to ask when an entire function f on E can be extended to an entire function on F.Firstly, by using the topological tensor product representation of polynormials on locally convex spaces, he proved that a polynomial f of integral type on E can be extended to a polynomial of integral type on F.Moreover, in case that E is a nuclear space, by using the above result he proved that an entire function f of uniform bounded type on E can be extended to an entire function F.This is an extension of Meise-Vogt' result(Proc.Amer.Math.Soc.1984).
Itokawa(INVESTIGATORS)investigated togather with Ryouich Kobayashi a famous conjecture that n-1 homology group on a complete non-compact manifold M with positive Ricci curvature is trivial, and showed that this conjecture is true in a lot of important cases. Moreover they succeeded in classifying n-1 homology group in case that M is a complete non-compact manifold M with non-negative Ricci curvature.
Nishibata(INVESTIGATORS)investigated hyperbolic-elliptic coupled systems and the discrete Bolzmann equation. For these equations they investigated the existence and uniqueness of solutions and the non-existence of classical solutions with certain conditions.
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