Project/Area Number  03640147 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
解析学

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
NISHIWADA Kimimasa Kyoto University, Integrated Human Studies Assistant Professor, 総合人間学部, 助教授 (60093291)

CoInvestigator(Kenkyūbuntansha) 
MORIMOTO Yoshinori Kyoto University, Graduate School of Human and Environmental Studies, Assistant, 人間環境学研究科, 助教授 (30115646)
KONO Norio Kyoto University, Integrated Human Studies Professor, 総合人間学部, 教授 (90028134)
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)
NISHIYAMA Kyo Kyoto University, Integrated Human Studies Assistant Professor, 総合人間学部, 助教授 (70183085)
KATO Shinichi Kyoto University, Integrated Human Studies Assistant Professor, 総合人間学部, 助教授 (90114438)
KASAHARA Koji Kyoto University, Integrated Human Studies Professor, 総合人間学部, 教授 (70026748)

Project Fiscal Year 
1991 – 1992

Project Status 
Completed(Fiscal Year 1992)

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)

Keywords  Schrodinger operator / Hypoellipticity / Eigenvalue estimate / Representation theory / Hecke algebra / Self similar process / Sample paths / Lie superalgebra / Schrodinger型作用素 / 準楕円性 / 固有値評価 / 表現論 / ヘッケ環 / 自己相似過程 / 見本関数 / Lie超代数 / ガウス算術幾何平均 / モノドロミ表現 / 楕円積分 
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 FeffermanPhong 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.
