# The Pompeiu Formula for Slice Hyperholomorphic Functions

## Document Type

Article

## Publication Date

2011

## Abstract

The fundamental result that makes complex analysis into a new discipline, independent from the theory of real variables, is the Cauchy formula, which allows the representation of any holomorphic function through a reproducing holomorphic kernel. This result is in fact an almost immediate application of the Stokes formula, which, in the more general case, offers an integral representation formula for c1 functions. This general representation formula is often known as the Pompeiu formula and can be stated as follows.

## Recommended Citation

Colombo, Fabrizio; Sabadini, Irene; Struppa, Daniel. The Pompeiu formula for slice hyperholomorphic functions. *The Michigan Mathematical Journal* 60 (2011), no. 1, 163--170. doi:10.1307/mmj/1301586309

## Peer Reviewed

1

## Copyright

University of Michigan, Department of Mathematics

## Comments

This article was originally published in

The Michigan Mathematical Journal, volume 60, issue 1, in 2011. DOI: 10.1307/mmj/1301586309