| Project/Area Number |
03640147
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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 | KYOTO UNIVERSITY |
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Principal Investigator |
NISHIWADA Kimimasa Kyoto University, Integrated Human Studies Assistant Professor, 総合人間学部, 助教授 (60093291)
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| Co-Investigator(Kenkyū-buntansha) |
MORIMOTO Yoshinori Kyoto University, Graduate School of Human and Environmental Studies, Assistant, 人間環境学研究科, 助教授 (30115646)
NISHIYAMA Kyo Kyoto University, Integrated Human Studies Assistant Professor, 総合人間学部, 助教授 (70183085)
KATO Shin-ichi Kyoto University, Integrated Human Studies Assistant Professor, 総合人間学部, 助教授 (90114438)
KONO Norio Kyoto University, Integrated Human Studies Professor, 総合人間学部, 教授 (90028134)
KASAHARA Koji Kyoto University, Integrated Human Studies Professor, 総合人間学部, 教授 (70026748)
宇敷 重広 京都大学, 教養部, 助教授 (10093197)
上田 哲生 京都大学, 教養部, 助教授 (10127053)
浅野 潔 京都大学, 教養部, 教授 (90026774)
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| Project Period (FY) |
1991 – 1992
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| Project Status |
Completed (Fiscal Year 1992)
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| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1992: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1991: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | Schrodinger operator / Hypoellipticity / Eigenvalue estimate / Representation theory / Hecke algebra / Self similar process / Sample paths / Lie superalgebra / ガウス算術幾何平均 / モノドロミ-表現 / 楕円積分 |
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| Research Abstract |
The aim of this project consists in doing research on the structure of solutions of hyperbolic equations and related problems in the theory of differential eauations. In so doing our project needs results not only from the theory of partial differential equations but also from a wide range of mathematical branches such as the function theory, the representation theory , the theory of stochastic process etc.. In more concrete terms [1] is concerned with certain L^2 estimates, which were used by Fefferman-Phong in order to get some eigenvalue estimates for the Schrodinger equation -DELTA+V(chi) . We used these estimates to prove the existence of certain degenerate hypoelliptic operators of general order. In [2] we discuss recent developments on random fields and their sample paths, where particular emphasis is given on self similar processes. The treatise is based on our survey lecture at the National University of Taiwan. In [3] it is proved that the duality for representations of a Hecke algebra is given by its automorphisms. In [4] is obtained a complete classification of all the unitary representations of the Lie superalgebra su(rho,q/n)and at the same time using a theory of super duality we give a concrete construction of the unitary representation on a Fock space. With this study one also obtains some examples of partial differential operators with values in the Clifford algebra and of some invariant forms. This paper utilizes the fact that the unitary representation of the Lie superalgebra is the highest weight representation.
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