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Moscow Mathematical Journal, 2017, Volume 17, Number 1, Pages 129–143
DOI: https://doi.org/10.17323/1609-4514-2017-17-1-129-143 (Mi mmj629) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
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DOI: https://doi.org/10.17323/1609-4514-2017-17-1-129-143
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.
Received: November 11, 2015
Bibliographic databases:
Document Type: Article
MSC: 30G35, 33C10, 44A12
Language: English
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
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\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
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\crossref{https://doi.org/10.17323/1609-4514-2017-17-1-129-143}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3634524}
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    • This publication is cited in the following 2 articles:
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