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Mosc. Math. J., 2017, Volume 17, Number 1, Pages 129–143 (Mi mmj629)  

On two-sided monogenic functions of axial type

Dixan Peña Peñaa, Irene Sabadinia, Frank Sommenb

a 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.

Funding Agency Grant Number
Istituto Nazionale di Alta Matematica "Francesco Severi"
D. Peña Peña acknowledges the support of a Postdoctoral Fellowship given by Istituto Nazionale di Alta Matematica (INdAM) and cofunded by Marie Curie actions.


DOI: https://doi.org/10.17323/1609-4514-2017-17-1-129-143

Full text: http://www.mathjournals.org/.../2017-017-001-008.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 30G35, 33C10, 44A12
Received: November 11, 2015
Language:

Citation: Dixan Peña Peña, Irene Sabadini, Frank Sommen, “On two-sided monogenic functions of axial type”, Mosc. Math. J., 17:1 (2017), 129–143

Citation in format AMSBIB
\Bibitem{PenSabSom17}
\by Dixan~Pe\~na Pe\~na, Irene~Sabadini, Frank~Sommen
\paper On two-sided monogenic functions of axial type
\jour Mosc. Math.~J.
\yr 2017
\vol 17
\issue 1
\pages 129--143
\mathnet{http://mi.mathnet.ru/mmj629}
\crossref{https://doi.org/10.17323/1609-4514-2017-17-1-129-143}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3634524}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000402641900008}


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