Title

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.

Comments

This article was originally published in The Michigan Mathematical Journal, volume 60, issue 1, in 2011. DOI: 10.1307/mmj/1301586309

Peer Reviewed

1

Copyright

University of Michigan, Department of Mathematics