English

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.

Keywords

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"

R2 v1 2026-06-22T06:09:15.096Z