The Cauchy problem in spaces of entire functions
type: Item
instance of: scholarly article
title: The Cauchy problem in spaces of entire functions
zbMATH Open document ID: 0858.35001
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1997-03-23T00:00:00Z
review text: In the first part we are interested in the case of differential operators with constant coefficients. We show directly that the solution of the Cauchy problem is an entire function if the data are so. In the second part we study the case of a differential operator, the principal part of which has constant coefficients, first in the space of entire functions and then in the space of entire functions of finite order. The third part concerns the global Cauchy-Kowalevski problem. Our studies are restricted to Cauchy problems, the same approach permits analogous theorems for the Goursat problem. We reduce the proof of the theorems to the proof of the fixed-point theorem in Banach spaces that we define by means of majorant functions.
Mathematics Subject Classification ID: 35A10
Mathematics Subject Classification ID: 30D20
Mathematics Subject Classification ID: 35E15
zbMATH DE Number: 917932
zbMATH Keywords: fixed-point theorem
author: Patrice Pongérard
author: Claude Wagschal
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 917932