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.

该项目的目的在于研究双曲方程解的结构以及微分方程理论中的相关问题。为此，我们的项目不仅需要偏微分方程理论的结果，还需要广泛的数学分支的结果，例如函数论、表示论、随机过程理论等。更具体地说 [1]与某些 L^2 估计有关，Fefferman-Phong 使用这些估计来获得薛定谔方程 -DELTA+V(chi) 的一些特征值估计。我们使用这些估计来证明某些一般阶简并亚椭圆算子的存在。在[2]中，我们讨论了随机场及其样本路径的最新发展，其中特别强调自相似过程。这篇论文是基于我们在台湾国立大学的调查讲座。在[3]中证明了赫克代数表示的对偶性是由其自同构给出的。在[4]中获得了李超代数su(rho,q/n)的所有酉表示的完整分类，同时使用超对偶性理论我们给出了Fock空间上酉表示的具体构造。通过这项研究，我们还获得了一些具有克利福德代数值和一些不变形式的偏微分算子的例子。本文利用了李超代数的酉表示是最高权重表示的事实。