Global differential equations for slice regular functions

In the present paper, we give a system of global differential equations which are satisfied by slice regular functions on a real alternative algebra. By means of the concepts of stem function and slice function, we are able to improve some results obtained recently in the quaternionic and slice mono...

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Bibliographic Details
Published in:Mathematische Nachrichten Vol. 287; no. 5-6; pp. 561 - 573
Main Authors: Ghiloni, Riccardo, Perotti, Alessandro
Format: Journal Article
Language:English
Published: Weinheim Blackwell Publishing Ltd 01.04.2014
Wiley Subscription Services, Inc
Subjects:
13J30
30C15
30G35
32A30
functions of a hypercomplex variable
global differential operators
Slice regular functions
ISSN:0025-584X, 1522-2616
Online Access:Get full text
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Summary:In the present paper, we give a system of global differential equations which are satisfied by slice regular functions on a real alternative algebra. By means of the concepts of stem function and slice function, we are able to improve some results obtained recently in the quaternionic and slice monogenic case and to extend them to this general setting. In particular, we describe the precise relation existing between the global differential equations and the condition of slice regularity.
Bibliography:ark:/67375/WNG-13TQXQN7-X
istex:E5CB0D5E6C993E4CDA8AA4BC32DC4E5E0F65467E
ArticleID:MANA201200318
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201200318