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Title: Riemann–Hilbert Problems for Monogenic Functions on Upper Half Ball of R^4
Author: Ku, Min
Wang, Ying
He, Fuli
Kähler, Uwe
Keywords: Riemann–Hilbert problems, Generalized Cauchy–Riemann equation, Quaternion analysis
Issue Date: 19-May-2017
Publisher: Birkhaeuser
Abstract: In this paper we are interested in finding solutions to Riemann– Hilbert boundary value problems, for short Riemann–Hilbert problems, with variable coefficients in the case of axially monogenic functions defined over the upper half unit ball centred at the origin in four-dimensional Euclidean space. Our main idea is to transfer Riemann– Hilbert problems for axially monogenic functions defined over the up- per half unit ball centred at the origin of four-dimensional Euclidean spaces into Riemann–Hilbert problems for analytic functions defined over the upper half unit disk of the complex plane. Furthermore, we extend our results to axially symmetric null-solutions of perturbed generalized Cauchy–Riemann equations.
Peer review: yes
DOI: 10.1007/s00006-017-0789-8
ISSN: 0188-7009
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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