This article is cited in 2 papers

On two-sided monogenic functions of axial type

Dixan Peña Peña^a, Irene Sabadini^a, Frank Sommen<sup>b

a</sup> Dipartimento di Matematica, Politecnico di Milano, Via E. Bonardi 9, 20133 Milano, Italy
^b Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering and Architecture, Ghent University, Galglaan 2, 9000 Gent, Belgium

Abstract: 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.

Key words and phrases: two-sided monogenic functions, plane waves, Vekua systems, Funk–Hecke's formula.

MSC: 30G35, 33C10, 44A12

Received: November 11, 2015

Language: English

DOI: 10.17323/1609-4514-2017-17-1-129-143

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