A Study on the Theory of Functions of Several Complex Variables and Analytic Differential Equations

代表人物Kajiwara做了无穷维复分析，首次证明了关于域的解析自同构行为的解析延拓原理在无穷维情况下也能实现，即证明了一个具有良好边界的域在边界点的邻域内与一个开球局部重合，且与该球全局重合。其次，将解析线性微分算子S和T在z复平面和w复平面上的合成ST满射性的条件分别约化为S和T在参数空间上的局部性。第三，研究了喷气发动机叶片的颤振分析，建立了求解复系数高阶代数方程组的真实的解的方法。利用留数定理和围道积分，编制了一个程序，以便在超级计算机上求得数值解。分享者Yosida研究了与几种复杂结构相关的解析线性偏微分方程，发现了描述几种重要代数簇族的方程，并阐明了结构。

The representative Kajiwara did Infinite Dimensional Complex Analysis and showed firstly that the principle of analytic prolongation concerning behavior of analytic automorphisms of domains accomplishes in case of infinite dimension, that is, he proves that a domain with good boundary coinciding locally with an open ball in a neighborhood of a boundary point coincides globally with the ball. Secondly, he reduces the condition of surjectivity of the composition ST of analytic linear differential operatos S and T in the z and w complex plains respectively to the locality of S and T in parameter spaces. Thirdly,he works on the Flutter Analysis of blades of jet engines, establishes a method of seeking real solutions of algebraic equations of complex coefficients and of higher order. making use of the residue theorem and contour integrals and obtains a program in order to obtain numerical solutions by a super computer. The sharer Yosida investigates analytic linear partial differential equations associated to several complex structures, finds equations which describes several important kinds of families of algebraic varieties and elucidates the structures.