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

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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.