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Global differential equations for slice regular functions
Author(s) -
Ghiloni Riccardo,
Perotti Alessandro
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200318
Subject(s) - mathematics , differential equation , function (biology) , relation (database) , algebra over a field , differential (mechanical device) , wafer , mathematical analysis , pure mathematics , computer science , data mining , electrical engineering , evolutionary biology , engineering , biology , aerospace engineering
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.