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The Fueter primitive of biaxially monogenic functions

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  • 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.
    Mathematics Subject Classification: Primary: 30G35.


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