Extension results for slice regular functions of a quaternionic variable

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 + y I can be recovered by the values of f at the points q + y J and q + y K for any choice of imaginary units I , J , K . This result allows us t...

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Bibliographic Details
Published in:	Advances in mathematics (New York. 1965) Vol. 222; no. 5; pp. 1793 - 1808
Main Authors:	Colombo, Fabrizio, Gentili, Graziano, Sabadini, Irene, Struppa, Daniele
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.12.2009
Subjects:	Functions of complex variables Functions of hypercomplex variables 30G35 Functions of hypercomplex variables Functions of complex variables
ISSN:	0001-8708, 1090-2082
Online Access:	Get full text
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Summary:	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 + y I can be recovered by the values of f at the points q + y J and q + y K 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.
ISSN:	0001-8708 1090-2082
DOI:	10.1016/j.aim.2009.06.015