CONSTRUCTION OF ANALYSIS ON COMPLEX MANIFOLD

1. (1)利用解析泛函理论给出了拉马努金积分公式和拉马努金求和公式的意义。特别阐明了拉毛扬积分公式与抽样定理的关系。(2)研究了解析泛函b在实球、复球和李球上的结构。(1)考虑了Fuchujan偏微分方程解的唯一性，(2)考虑了偏微分方程形式解的Gevrey渐近性质，(3)考虑了Davey-Stewartson的性质。确定了对称空间中的共形群、轨道分解。完成了分级李代数的重构。确定了与黎曼对称空间相关的Zeta函数和Shintani函数。提出了可视化斯托克斯线的计算机方法（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.