On the representation of generalized analytic vectors
type: Item
instance of: scholarly article
title: On the representation of generalized analytic vectors
zbMATH Open document ID: 0829.35017
DOI: 10.4171/ZAA/631
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1995-09-25T00:00:00Z
review text: Summary: This paper is concerned with the representation of generalized analytic vectors which are defined as solutions of certain elliptic systems of linear first-order partial differential equations in two complex variables. For the explicite representation of solutions we give integral operators of Vekua type as well as differential operators of Bauer type which map holomorphic vectors onto the set of solutions. For the existence of the differential operators we give a necessary and sufficient condition. We discuss properties of these operators and show how to construct the kernels of the integral operators using the differential operators. Finally we present examples for systems of differential equations for which all the solutions can be represented explicitly.
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35J45
Mathematics Subject Classification ID: 30G20
Mathematics Subject Classification ID: 35C10
zbMATH DE Number: 800338
zbMATH Keywords: generalized analytic vectors
zbMATH Keywords: integral operators of Vekua type
author: Peter Berglez
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 800338