The Cauchy transform in the slice hyperholomorphic setting and related topics
Complex Variables
2019-01-30 v1
Abstract
In this paper we study the additive splitting associated to the quaternionic Cauchy transform defined by the Cauchy formula of slice hyperholomorphic functions. Moreover, we introduce and study the analogue of the fundamental solution of the global operator of slice hyperholomorphic functions. We state our results in the quaternionic setting but several results hold for Clifford algebra-valued function with minor changes in the proofs.
Keywords
Cite
@article{arxiv.1804.10903,
title = {The Cauchy transform in the slice hyperholomorphic setting and related topics},
author = {Fabrizio Colombo and Samuele Mongodi},
journal= {arXiv preprint arXiv:1804.10903},
year = {2019}
}