On Diophantine properties for convergence of formal solutions
type: Item
instance of: scholarly article
title: On Diophantine properties for convergence of formal solutions
zbMATH Open document ID: 0598.35012
author: Masafumi Yoshino
published in: Proceedings of the Japan Academy. Series A
publication date: 1986-01-01T00:00:00Z
review text: The author presents a theorem which gives a necessary and sufficient criterion for the convergence of all formal solutions of a partial differential equation \(P(x;\partial)u=f(x)x^{\omega}\), (\(\omega\in {\mathbb{C}}\), f analytic), in two variables \(x_ 1,x_ 2\). The short note also contains some remarks and two corollaries, but for details the author refers to a preprint of another paper.
Mathematics Subject Classification ID: 35A99
Mathematics Subject Classification ID: 35C10
zbMATH DE Number: 3964463
zbMATH Keywords: formal solutions
reviewed by: Wolfgang Watzlawek
MaRDI profile type: Publication
full work available at URL: pjaa.62.49
OpenAlex ID: W2084770331
cites work: On a class of linear partial differential equations whose formal solutions always converge
cites work: Caractere non fredholmien du problème de Goursat
cites work: Une fonction de la théorie des nombres
cites work: Q5813396
cites work: The diophantine nature for the convergence of formal solutions
DOI: 10.3792/PJAA.62.49
description: scientific article; zbMATH DE number 3964463