Extension results for slice regular functions of a quaternionic variable

Details Extension results for slice regular functions of a quaternionic variable Extension results for slice regular functions of a quaternionic variable

2009-05-12

arxiv.org/abs/0905.1861v1

Adv. Math. 222 (2009), no. 5, 1793--1808

Mathematics

Complex Variables

Scientific paper

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 $q=x+yI$ can be recovered by the values of $f$ at the points $q+yJ$ and $q+yK$ for any choice of imaginary units $I, J, K.$ 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.

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