The Fueter primitive of biaxially monogenic functions

Fabrizio Colombo; Irene Sabadini; Frank Sommen

doi:10.3934/cpaa.2014.13.657

Article Contents

2014, Volume 13, Issue 2: 657-672. Doi: 10.3934/cpaa.2014.13.657

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The Fueter primitive of biaxially monogenic functions

1.
Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano
2.
Politecnico di Milano, Dipartimento di Matematica, Via Bonardi, 9, 20133 Milano
3.
Clifford Research Group, Faculty of Sciences, Ghent University, Galglaan 2, 9000 Gent

Received: January 31, 2013

Revised: June 30, 2013

Published: February 2014

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Abstract

In the recent papers by F. Colombo, I. Sabadini, F. Sommen, "The inverse Fueter mapping theorem", Commun. Pure Appl. Anal., 10 (2011), 1165--1181, and "The inverse Fueter mapping theorem in integral form using spherical monogenics", Israel J. Math., 194 (2013), 485--505, the authors have started a systematic study of the inverse Fueter mapping theorem. In this paper we show that the inversion theorem holds for the case of biaxially monogenic functions. Here there are several additional difficulties with respect to the cases already treated. However, we are still able to prove an integral version of the inverse Fueter mapping theorem. The kernels appearing in the integral representation formula have an explicit representation that can be computed depending on the dimension of the Euclidean space in which the problem is considered.

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Mathematics Subject Classification: Primary: 30G35.

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