A Cauchy kernel for slice regular functions
Complex Variables
2010-03-30 v1
Abstract
In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the expression of the derivatives of a regular function in terms of the powers of the Cauchy kernel, and we present several other consequent results.
Cite
@article{arxiv.0902.4771,
title = {A Cauchy kernel for slice regular functions},
author = {Fabrizio Colombo and Graziano Gentili and Irene Sabadini},
journal= {arXiv preprint arXiv:0902.4771},
year = {2010}
}