| Project/Area Number |
01540160
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | Waseda University |
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Principal Investigator |
WADA Junzo Waseda University Dept. of Math. Professor (School of Education), 教育学部, 教授 (50063342)
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| Co-Investigator(Kenkyū-buntansha) |
KORI Toshiaki Waseda University Dept. of Math. Professor (School of Su and Eng.), 理工学部, 教授 (50063730)
SUZUKI Shin'ichi Waseda University Dept. of Math. Professor (School of Education), 教育学部, 教授 (10030777)
ISHIGAKI Haruo Waseda University Dept. of Math. Professor (School of Education), 教育学部, 教授 (60063492)
HINOHARA Yukitoshi Waseda University Dept. of Math. Professor (School of Education), 教育学部, 教授 (10063471)
MIYADERA Isao Waseda University Dept. of Math. Professor (School of Education), 教育学部, 教授 (50063293)
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| Project Period (FY) |
1989 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| Budget Amount *help |
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1990: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1989: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | Function spaces / Analytic functions / Function algebras / Strictly pseudo-convex domains / Semigroups / Cー半群 / Grassman多様体 / C-半群 |
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| Research Abstract |
The contents of our project consist of theory of function spaces and its applications.
1. The theory. We study function spaces, especially function spaces consisting of analytic functions and function algebras. J. Wada (with S. Yamaguchi) studies peak sets for function spaces and gives characterizations to assert that A=C(X) for function spaces on a compact Hausdorff space X having some conditions connected with peak sets. Especially he establishes generalizations of a theorem of Rudin and a theorem of Hoffman and Wermer. Also, T. Kori gives a characterization of the dual space of the space A(D) of functions which are continuous on and holomorphic on D, where D is a bounded strictly pseudo-convex domain in C^n.
2. Its applications. We study generalized function spaces, that is, vector-valued function spaces and spaces of functions defined on more general spaces. I. Miyadera (with N. Tanaka) publishes a lot of papers on semigroups of linear operators on Banach spaces. One of them is a generalization of the Hille-Yosida theorem. As a generalization of the theorem relative to generation of semigroups of class (Co), he investigates a theory of generation of integrated C-semigroups.
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