A local Cauchy integral formula for slice-regular functions
Complex Variables
2023-10-16 v1
Abstract
We prove a Cauchy-type integral formula for slice-regular functions where the integration is performed on the boundary of an open subset of the quaternionic space, with no requirement of axial symmetry. In particular, we get a local Cauchy-type integral formula. As a step towards the proof, we provide a decomposition of a slice-regular function as a combination of two axially monogenic functions.
Cite
@article{arxiv.2105.07041,
title = {A local Cauchy integral formula for slice-regular functions},
author = {Alessandro Perotti},
journal= {arXiv preprint arXiv:2105.07041},
year = {2023}
}