Extension Results for Slice Regular Functions of a Quaternionic Variable

Authors

Fabrizio Colombo, Politecnico di Milano
Graziano Gentili, University of FlorenceFollow
Irene Sabadini, Politecnico di Milano
Daniele C. Struppa, Chapman UniversityFollow

Document Type

Article

Publication Date

2009

Abstract

In this paper we prove a new Representation Formula for slice regular functions, which shows that the value of a slice regular function f at a point q=x+yIq=x+yI can be recovered by the values of f at the points q+yJq+yJ and q+yKq+yK for any choice of imaginary units I,J,KI,J,K. This result allows us to extend the known properties of slice regular functions defined on balls centered on the real axis to a much larger class of domains, called axially symmetric domains. We show, in particular, that axially symmetric domains play, for slice regular functions, the role played by domains of holomorphy for holomorphic functions.

Comments

This article was originally published in Advances in Mathematics, volume 222, issue 5, in 2009. DOI: 10.1016/j.aim.2009.06.015

Recommended Citation

Colombo, F., Gentili, G., Sabadini, I., & Struppa, D. (2009). Extension results for slice regular functions of a quaternionic variable. Advances in Mathematics, 222(5), 1793-1808. doi: 10.1016/j.aim.2009.06.015

Peer Reviewed

1

Copyright

Elsevier