Holomorphicity of slice-regular functions
Abstract
Slice-regular functions of a quaternionic variable have been studied extensively in the last 12 years, resulting, in many ways, quite close to classical holomorphic functions of a complex variable; indeed, there is a correspondence between slice-regular functions and a certain family of holomorphic maps from the complex plane to , as noted by Ghiloni and Perotti. However, such a construction does not seem to offer any insight on the behaviour of slice-regular functions, due to the lack of a connection between the values of the holomorphic map and the values of the associated sliceregular function. The aim of this work is to show that there is indeed a (complex) geometric way to relate the values of this two functions, thus relating more deeply the world of holomorphic functions with that of slice-regular functions.
Cite
@article{arxiv.1807.05899,
title = {Holomorphicity of slice-regular functions},
author = {Samuele Mongodi},
journal= {arXiv preprint arXiv:1807.05899},
year = {2018}
}