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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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
2007-12-01
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| Series: | Le Matematiche |
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| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/26 |
| _version_ | 1818151966332682240 |
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| author | Peter Berglez |
| author_facet | Peter Berglez |
| author_sort | Peter Berglez |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-11T13:47:13Z |
| format | Article |
| id | doaj.art-ecff4e52ea774a6888e6cf222900f7ad |
| institution | Directory Open Access Journal |
| issn | 0373-3505 2037-5298 |
| language | English |
| last_indexed | 2024-12-11T13:47:13Z |
| publishDate | 2007-12-01 |
| publisher | Università degli Studi di Catania |
| record_format | Article |
| series | Le Matematiche |
| spelling | doaj.art-ecff4e52ea774a6888e6cf222900f7ad2022-12-22T01:04:28ZengUniversità 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 |
| spellingShingle | Peter Berglez On generalized derivatives and formal powers for pseudoanalytic functions Le Matematiche Pseudoanalytic functions Generalized (F,G)-derivative Formal powers |
| title | 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_short | On generalized derivatives and formal powers for pseudoanalytic functions |
| title_sort | on generalized derivatives and formal powers for pseudoanalytic functions |
| 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 |