naa a22 4500 510783333 CHVBK 20180411083254.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s11856-012-0090-4 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0090-4 The inverse Fueter mapping theorem in integral form using spherical monogenics [Elektronische Daten] [Fabrizio Colombo, Irene Sabadini, Franciscus Sommen] In this paper we prove an integral representation formula for the inverse Fueter mapping theorem for monogenic functions defined on axially symmetric open sets U ⊆ ℝ n+1, i.e. on open sets U invariant under the action of SO(n), where n is an odd number. Every monogenic function on such an open set U can be written as a series of axially monogenic functions of degree k, i.e. functions of type $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{f} _k (x) = \left[ {A\left( {x_{0,\rho } } \right) + \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\omega } {\rm B}\left( {x_{0,\rho } } \right)} \right]\mathcal{P}_k (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} )$$ , where A(x 0, ρ) and B(x 0, ρ) satisfy a suitable Vekua-type system and $$\mathcal{P}_k (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} )$$ is a homogeneous monogenic polynomial of degree k. The Fueter mapping theorem says that given a holomorphic function f of a paravector variable defined on U, then the function $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{f} _k (x)\mathcal{P}_k (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} )$$ given by $$\Delta ^{k + \tfrac{{n - 1}} {2}} \left( {f(x)\mathcal{P}_k (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} )} \right) = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{f} (x)\mathcal{P}_k (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} )$$ is a monogenic function. The aim of this paper is to invert the Fueter mapping theorem by determining a holomorphic function f of a paravector variable in terms of $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{f} _k (x)\mathcal{P}_k (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} )$$ . This result allows one to invert the Fueter mapping theorem for any monogenic function defined on an axially symmetric open set. Hebrew University Magnes Press, 2012 Colombo Fabrizio Politecnico di Milano, Dipartimento di Matematica, Via Bonardi, 9, 20133, Milano, Italy aut Sabadini Irene Politecnico di Milano, Dipartimento di Matematica, Via Bonardi, 9, 20133, Milano, Italy aut Sommen Franciscus Clifford Research Group, Faculty of Sciences, Ghent University Galglaan 2, 9000, Gent, Belgium aut Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 485-505 0021-2172 194:1<485 2013 194 11856 https://doi.org/10.1007/s11856-012-0090-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0090-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Colombo Fabrizio Politecnico di Milano, Dipartimento di Matematica, Via Bonardi, 9, 20133, Milano, Italy aut NATIONALLICENCE 700 1- Sabadini Irene Politecnico di Milano, Dipartimento di Matematica, Via Bonardi, 9, 20133, Milano, Italy aut NATIONALLICENCE 700 1- Sommen Franciscus Clifford Research Group, Faculty of Sciences, Ghent University Galglaan 2, 9000, Gent, Belgium aut NATIONALLICENCE 773 0- Israel Journal of Mathematics The Hebrew University Magnes Press 194/1(2013-03-01), 485-505 0021-2172 194:1<485 2013 194 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer