Differentialoperatoren bei partiellen Differentialgleichungen
type: Item
instance of: scholarly article
title: Differentialoperatoren bei partiellen Differentialgleichungen
zbMATH Open document ID: 0607.35054
DOI: 10.1007/BF01769214
author: Peter Berglez
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1986-01-01T00:00:00Z
review text: Those formally hyperbolic differential equations are characterized for which solutions can be represented by means of differential operators acting on holomorphic functions. This is done by a necessary and sufficient condition on the coefficients of the differential equation. These operators are determined simultaneously. By it a general procedure is presented to construct differential equations and corresponding differential operators which map holomorphic functions onto solutions of the differential equations. We also discuss the question under which circumstances all the solutions of a differential equation can be represented by differential operators. For the equations characterized previously we determine the Riemann function. Some special classes of differential equations are investigated in detail. Furthermore the possibility of a representation of pseudo-analytic functions and the corresponding Vekua resolvents by differential operators is discussed.
Mathematics Subject Classification ID: 35L10
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35A20
zbMATH DE Number: 3981677
zbMATH Keywords: differential operators
zbMATH Keywords: holomorphic functions
zbMATH Keywords: coefficients of the differential equation
zbMATH Keywords: Riemann function
zbMATH Keywords: representation
zbMATH Keywords: pseudo-analytic functions
zbMATH Keywords: Vekua resolvents
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3981677