Notions of Regularity for Functions of a Split-Quaternionic Variable
Complex Variables
2015-06-25 v1
Abstract
Notions of a "holomorphic" function theory for functions of a split-quaternionic variable have been of recent interest. We describe two found in the literature and show that one notion encompasses a small class of functions, while the other gives a richer collection. In the second instance, we describe a simple subclass of functions and give two examples of an analogue of the Cauchy-Kowalewski extension in this context.
Cite
@article{arxiv.1506.07481,
title = {Notions of Regularity for Functions of a Split-Quaternionic Variable},
author = {John A. Emanuello and Craig A. Nolder},
journal= {arXiv preprint arXiv:1506.07481},
year = {2015}
}