权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Structure of solutions of the hyperbolic equation

双曲方程解的结构

基本信息

批准号：
03640147
负责人：
NISHIWADA Kimimasa
金额：
$ 1.09万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1992
项目状态：
已结题

项目摘要

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.

本课题旨在研究双曲方程解的结构及微分方程理论中的相关问题。因此，我们的项目不仅需要来自偏微分方程理论的结果，还需要来自广泛的数学分支，如函数理论、表示理论、随机过程理论等。更具体地说，[1]与某些L^2估计有关，这些估计被Fefferman-Phong用来获得薛定谔方程-DELTA+V（chi）的一些特征值估计。利用这些估计证明了一类一般阶简并次椭圆算子的存在性。在b[2]中，我们讨论了随机场及其样本路径的最新进展，其中特别强调了自相似过程。在[3]中证明了Hecke代数的对偶表示是由它的自同构给出的。在[4]中得到了李超代数su（rho,q/n）的所有酉表示的完全分类，同时利用超对偶理论给出了Fock空间上的酉表示的具体构造。在此基础上，我们还得到了一些具有Clifford代数值的偏微分算子的例子和一些不变形式的例子。本文利用李超代数的酉表示是最高权表示的事实。