| 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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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2000: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1999: ¥3,200,000 (Direct Cost: ¥3,200,000)
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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 / 局所凸空間 / 位相テンソル積表現 / 一様有界型 / 離散型方程式 / 核形空間 / 一様有界型正則写像 / 正則拡大 / π-位相 / ε-位相 / 積分型写像 / Weak Typeの正則写像 |
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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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