On two-sided monogenic functions of axial type

2016/09/25 by Dixan Peña Peña, Peña, Dixan Peña, Irene Sabadini +3
Mathematics · #30G35 #33C10 #44A12 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30G35 #msc:33C10 #msc:44A12

paper · pdf · doi:10.48550/arxiv.1609.07794

17 pages, accepted for publication in Moscow Mathematical Journal

arxiv created 2016/09/25 · arxiv updated 2016/09/27

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.

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