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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Runge theorem for slice hyperholomorphic functions


Authors: Fabrizio Colombo, Irene Sabadini and Daniele C. Struppa
Journal: Proc. Amer. Math. Soc. 139 (2011), 1787-1803
MSC (2010): Primary 30G35; Secondary 30B10, 30C10
Published electronically: December 13, 2010
MathSciNet review: 2763766
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Abstract: In this paper we introduce and study rational slice monogenic functions. After proving a decomposition theorem for such functions, we are able to prove the Runge approximation theorem for slice monogenic functions. We then show how a similar argument can be used to obtain an analogue of the Runge approximation theorem in the slice regular setting.


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Additional Information

Fabrizio Colombo
Affiliation: Dipartimento di Matematica, Politecnico di Milano, Via Bonardi, 9, 20133 Milano, Italy
Email: fabrizio.colombo@polimi.it

Irene Sabadini
Affiliation: Dipartimento di Matematica, Politecnico di Milano, Via Bonardi, 9, 20133 Milano, Italy
Email: irene.sabadini@polimi.it

Daniele C. Struppa
Affiliation: Department of Mathematics, Schmid College of Science, Chapman University, Orange, California 92866
Email: struppa@chapman.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10812-2
PII: S 0002-9939(2010)10812-2
Received by editor(s): May 25, 2010
Published electronically: December 13, 2010
Communicated by: Franc Forstneric
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.