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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Runge theorem for slice hyperholomorphic functions
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by Fabrizio Colombo, Irene Sabadini and Daniele C. Struppa PDF
Proc. Amer. Math. Soc. 139 (2011), 1787-1803 Request permission

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
  • MR Author ID: 601509
  • Email: fabrizio.colombo@polimi.it
  • Irene Sabadini
  • Affiliation: Dipartimento di Matematica, Politecnico di Milano, Via Bonardi, 9, 20133 Milano, Italy
  • MR Author ID: 361222
  • Email: irene.sabadini@polimi.it
  • Daniele C. Struppa
  • Affiliation: Department of Mathematics, Schmid College of Science, Chapman University, Orange, California 92866
  • MR Author ID: 168380
  • ORCID: 0000-0002-3664-1729
  • Email: struppa@chapman.edu
  • Received by editor(s): May 25, 2010
  • Published electronically: December 13, 2010
  • Communicated by: Franc Forstneric
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 1787-1803
  • MSC (2010): Primary 30G35; Secondary 30B10, 30C10
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10812-2
  • MathSciNet review: 2763766