CONSTRUCTION OF ANALYSIS ON COMPLEX MANIFOLD

1.(1)利用解析泛函理论，给出了Ramanujan积分公式和Rananujan求和公式的含义。特别是阐明了Ramauujan积分公式与抽样定理之间的关系。(2)研究了实球、复球和李球上解析函数B的结构。(1)Fuchujan偏微分方程解的唯一性；(2)偏微分方程解的Gevrey渐近性态；(3)Davey-Stewartson解的渐近性。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对称空间上的Zeta函数和Shintani函数。发展了一种计算机可视化斯托克斯线的方法(这在复杂的WKB分析中很重要)。

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.