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The Fueter primitive of biaxially monogenic functions. (English) Zbl 1277.30036

Summary: In the recent papers [Commun. Pure Appl. Anal. 10, No. 4, 1165–1181 (2011; Zbl 1258.30022); Isr. J. Math. 194, Part A, 485–505 (2013; Zbl 1341.30042)], we 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.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
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