On generalized derivatives and formal powers for pseudoanalytic functions

We consider pseudoanalytic functions depending on two or three real variables. They are characterized by the corresponding Bers-Vekua equations. In the case of two dimensions we use the complex notation whereas for the case of three variables the concept of complex quaternions serves for our investi...

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Bibliographic Details
Main Author:	Peter Berglez
Format:	Article
Language:	English
Published:	Università degli Studi di Catania 2007-12-01
Series:	Le Matematiche
Subjects:	Pseudoanalytic functions Generalized (F,G)-derivative Formal powers
Online Access:	http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/26

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spelling	doaj-ecff4e52ea774a6888e6cf222900f7ad2020-11-25T02:25:01ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52982007-12-01622293624On generalized derivatives and formal powers for pseudoanalytic functionsPeter Berglez0Graz University of TechnologyWe consider pseudoanalytic functions depending on two or three real variables. They are characterized by the corresponding Bers-Vekua equations. In the case of two dimensions we use the complex notation whereas for the case of three variables the concept of complex quaternions serves for our investigations. In a particular plane case we give an explicit representation of formal powers with which a complete system of solutions of the corresponding Bers-Vekua equation can be given. By an example we show how the concept of formal powers may also be applied to the case of three variables.http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/26Pseudoanalytic functionsGeneralized (F,G)-derivativeFormal powers
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Peter Berglez
spellingShingle	Peter Berglez On generalized derivatives and formal powers for pseudoanalytic functions Le Matematiche Pseudoanalytic functions Generalized (F,G)-derivative Formal powers
author_facet	Peter Berglez
author_sort	Peter Berglez
title	On generalized derivatives and formal powers for pseudoanalytic functions
title_short	On generalized derivatives and formal powers for pseudoanalytic functions
title_full	On generalized derivatives and formal powers for pseudoanalytic functions
title_fullStr	On generalized derivatives and formal powers for pseudoanalytic functions
title_full_unstemmed	On generalized derivatives and formal powers for pseudoanalytic functions
title_sort	on generalized derivatives and formal powers for pseudoanalytic functions
publisher	Università degli Studi di Catania
series	Le Matematiche
issn	0373-3505 2037-5298
publishDate	2007-12-01
description	We consider pseudoanalytic functions depending on two or three real variables. They are characterized by the corresponding Bers-Vekua equations. In the case of two dimensions we use the complex notation whereas for the case of three variables the concept of complex quaternions serves for our investigations. In a particular plane case we give an explicit representation of formal powers with which a complete system of solutions of the corresponding Bers-Vekua equation can be given. By an example we show how the concept of formal powers may also be applied to the case of three variables.
topic	Pseudoanalytic functions Generalized (F,G)-derivative Formal powers
url	http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/26
work_keys_str_mv	AT peterberglez ongeneralizedderivativesandformalpowersforpseudoanalyticfunctions
_version_	1724853274279936000

On generalized derivatives and formal powers for pseudoanalytic functions

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