×

The inverse Fueter mapping theorem. (English) Zbl 1258.30022

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 \(f= \Delta^{{n-1\over 2}}f(x)\).

MSC:

30G35 Functions of hypercomplex variables and generalized variables
PDFBibTeX XMLCite
Full Text: DOI