Analytic Functions of a Quaternionic Variable
Functional Analysis
2008-04-02 v2 Complex Variables
Abstract
Here we follow the basic analysis that is common for real and complex variables and find how it can be applied to a quaternionic variable. Non-commutativity of the quaternion algebra poses obstacles for the usual manipulations; but we show how many of those obstacles can be overcome. After a tiny bit of linear algebra we look at the beginnings of differential calculus. The surprising result is that the first order term in the expansion of F(x+delta) is a compact formula involving both F'(x) and [F(x) - F(x*)]/(x-x*).
Keywords
Cite
@article{arxiv.0803.3782,
title = {Analytic Functions of a Quaternionic Variable},
author = {Charles Schwartz},
journal= {arXiv preprint arXiv:0803.3782},
year = {2008}
}
Comments
8 pages; added references and added Appendix B on SU(2)