Noncommutative Cauchy integral formula
Complex Variables
2016-02-12 v3
Abstract
The aim of this paper is to provide and prove the most general Cauchy integral formula for slice regular functions and for C^1 functions on a real alternative *-algebra. Slice regular functions represent a generalization of the classical concept of holomorphic function of a complex variable in the noncommutative and nonassociative settings. As an application, we obtain two kinds of local series expansion for slice regular functions.
Cite
@article{arxiv.1409.8455,
title = {Noncommutative Cauchy integral formula},
author = {Riccardo Ghiloni and Alessandro Perotti and Vincenzo Recupero},
journal= {arXiv preprint arXiv:1409.8455},
year = {2016}
}
Comments
13 pages, an example has been added at the end of Section 4. To appear in "Complex Analysis and Operator Theory"