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CONSTRUCTION OF ANALYSIS ON COMPLEX MANIFOLD

复杂流形分析的构建

基本信息

批准号：
08454035
负责人：
YOSINO Kunio
金额：
$ 4.61万
依托单位：
SOPHIA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1998
项目状态：
已结题

项目摘要

1. (1)The meaning of Ramanujan's integral formula and Rananujan' summation formula are given by using the theory of analytic functionajs. Especially, relation between Ramauujan's integral formula and sampling theorem is clarified. (2)The structure of analytic functionaiB on real sphere, complex sphere and Lie sphere are studied.2. (1)Uniqueness of solution to Fuchujan partial differential equations, (2)Gevrey asymptotic behavior of formal solutions of partial differential equations (3) Behavior of Davey-Stewartson are considered.3. Conformal group, orbit decomposition in symmetric spaces are determined. Reconstruction of graded Lie algebra are done.4. Zeta function associated to Riemaniann symmetric spaces and Shintani function are determined.5. Computer method to visualize the stokes line (which is important in complex WKB analysis) is developped.

1.（1）利用解析泛函理论给出了Ramanujan积分公式和Rananujan求和公式的意义。特别是阐明了Ramauujan积分公式与采样定理之间的关系。（2）研究了真实的球面、复球面和李球面上解析泛函B的结构.（1）Fuchujan型偏微分方程解的唯一性，（2）偏微分方程形式解的Gevrey渐近性，（3）Davey-Stewartson行为.确定了对称空间中的共形群、轨道分解。对分次李代数进行了重构.确定了Riemaniann对称空间的Zeta函数和Shintani函数.本文提出了一种用计算机显示斯托克斯线的方法，斯托克斯线在复杂的WKB分析中是很重要的。