Abstract. In this paper we investigate the new theory of slice regular functions of a quaternionic variable. We prove a new Representation Formula, 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.

Extension results for slice regular functions of a quaternionic variable / F.Colombo; G.Gentili; I.Sabadini; D.Struppa. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 222:(2009), pp. 1793-1808. [10.1016/j.aim.2009.06.015]

Extension results for slice regular functions of a quaternionic variable

GENTILI, GRAZIANO;
2009

Abstract

Abstract. In this paper we investigate the new theory of slice regular functions of a quaternionic variable. We prove a new Representation Formula, 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.
222
1793
1808
F.Colombo; G.Gentili; I.Sabadini; D.Struppa
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/359869
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