English

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.

Keywords

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}
}
R2 v1 2026-06-24T02:07:45.590Z