Some properties for quaternionic slice-regular functions on domains without real points

Abstract

The theory of slice regular functions over the quaternions, introduced by Gentili and Struppa in [5], was born on domains that intersect the real axis. This hypothesis can be overcome using the theory of stem functions introduced by Ghiloni and Perotti ([6]), in the context of real alternative algebras. In this paper I will recall the notion and the main properties of stem functions. After that I will introduce the class of slice regular functions induced by stem functions and, in this set, I will extend the identity principle, the maximum and minimum modulus principles and the open mapping theorem. Differences will be shown between the case when the domain does or does not intersect the real axis.

14 pages. first review. arXiv admin note: text overlap with arXiv:1008.4318 by other authors

Cited by in corpus (13)

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• Twistor interpretation of slice regular functions
• Geometric function theory over quaternionic slice domains
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• S-regular functions which preserve a complex slice
• Equivalence of slice semi-regular functions via Sylvester operators
• Slice regular functions as covering maps and global $\star$-roots
• Spherical coefficients of slice regular functions
• Quaternionic slice regularity beyond slice domains
• A unified theory of regular functions of a hypercomplex variable