Existence and continuation of holomorphic solutions of differential equations of infinite order
The author presents some results concerning existence and analytic continuation of holomorphic solutions of linear differential equations of infinite order. \textit{J. M. Bony} and \textit{P. Schapira} [Invent. Math. 17, 95-105 (1972; Zbl 0225.35008)] dealt with analytic continuation of the solutions of differential equations of finite order and also established local existence of solutions of the equations. The present author investigates these subjects when the equations are of infinite order. His method is to use the invertibility theorem for pseudodifferential operators of infinite order and the prolongation theorem of Kashiwara and Schapira.
scientific article; zbMATH DE number 4150987
scientific article