The Runge theorem for slice hyperholomorphic functions

Colombo, Fabrizio; Sabadini, Irene; Struppa, Daniele

doi:10.1090/S0002-9939-2010-10812-2

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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