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

代表人物Kajiwara做了无限维复分析，首次证明了关于区域的解析自同构行为的解析延拓原理在无限维情形下成立，即证明了边界良好的区域在边界点附近局部与开球重合的区域与球整体重合。其次，将z和w复平面上的解析线性微分算子S和T的合成ST的满足性条件分别简化为S和T在参数空间中的局部性。第三，研究了喷气发动机叶片的颤振分析，建立了求复系数高阶代数方程实数解的方法。利用留数定理和轮廓线积分，编制了程序，在超级计算机上进行数值求解。分享者Yosida研究了与几个复杂结构有关的解析线性偏微分方程组，找到了描述几类重要代数簇的方程，并阐明了这些结构。

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.