Existence and continuation of holomorphic solutions of differential equations of infinite order
type: Item
instance of: scholarly article
title: Existence and continuation of holomorphic solutions of differential equations of infinite order
zbMATH Open document ID: 0702.35253
DOI: 10.1016/0001-8708(88)90030-8
author: Takashi Aoki
published in: Advances in Mathematics
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35R50
Mathematics Subject Classification ID: 35S99
Mathematics Subject Classification ID: 35B60
zbMATH DE Number: 4150987
zbMATH Keywords: existence
zbMATH Keywords: analytic continuation
zbMATH Keywords: invertibility theorem
zbMATH Keywords: prolongation theorem
reviewed by: Hiroshi Haruki
MaRDI profile type: Publication
full work available at URL: 0001-8708(88)90030-8
OpenAlex ID: W1963559508
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description: scientific article; zbMATH DE number 4150987