Moscow Mathematical Journal

Volume 17, Issue 1, January–March 2017 pp. 129–143.

On Two-Sided Monogenic Functions of Axial Type

Authors: Dixan Peña Peña (1), Irene Sabadini (1), and Frank Sommen (2)
Author institution:(1) Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi 9, 20133 Milano, Italy
(2) Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering and Architecture, Ghent University, Galglaan 2, 9000 Gent, Belgium

Summary:

In this paper we study two-sided (left and right) axially symmetric solutions of a generalized Cauchy–Riemann operator. We present three methods to obtain special solutions: via the Cauchy–Kowalevski extension theorem, via plane wave integrals and Funk–Hecke's formula and via primitivation. Each of these methods is effective enough to generate all the polynomial solutions.

2010 Math. Subj. Class. 30G35, 33C10, 44A12.

Keywords: Two-sided monogenic functions, plane waves, Vekua systems, Funk–Hecke’s formula.

Contents Full-Text PDF