Colombo, Fabrizio; Sabadini, Irene; Sommen, Frank The inverse Fueter mapping theorem. (English) Zbl 1258.30022 Commun. Pure Appl. Anal. 10, No. 4, 1165-1181 (2011). The authors show how to give an integral representation of the Fueter mapping theorem using the Cauchy formula for slice monogenic functions. Specifically, given a slice monogenic function \(f\) of the form \(f= \alpha+\underline\omega\beta\), where \(\alpha\), \(\beta\) satisfy the Cauchy-Riemann equations, they represent in integral form the axially monogenic function \(\breve f= A+\underline\omega B\), where \(A\), \(B\) satisfy the Vekua’s system, given by \(\breve f(x)=\Delta^{{n-1\over 2}}f(x)\), where \(\Delta\) is the Laplace operator in dimension \(n+1\). In this paper the authors solve the inverse problem: given an axially monogenic function \(\breve f\) determine a slice monogenic function \(f\) (called Fueter’s primitive of \(\breve f\)) such that \(f= \Delta^{{n-1\over 2}}f(x)\). Reviewer: Miloš Čanak (Beograd) Cited in 1 ReviewCited in 28 Documents MSC: 30G35 Functions of hypercomplex variables and generalized variables Keywords:Cauchy-Riemann equations; Vekua’s system; axially monogenic function; slice monogenic functions; Fueter’s primitive PDFBibTeX XMLCite \textit{F. Colombo} et al., Commun. Pure Appl. Anal. 10, No. 4, 1165--1181 (2011; Zbl 1258.30022) Full Text: DOI