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Results in Mathematics

, Volume 63, Issue 3–4, pp 1375–1394 | Cite as

On the Riemann Boundary Value Problem for Null Solutions to Iterated Generalized Cauchy–Riemann Operator in Clifford Analysis

  • Paula Cerejeiras
  • Uwe Kähler
  • Min KuEmail author
Article

Abstract

In this paper we consider a kind of Riemann boundary value problem (for short RBVP) for null solutions to the iterated generalized Cauchy–Riemann operator and the polynomially generalized Cauchy–Riemann operator, on the sphere of \({\mathbb{R}^{n+1}}\) with Hölder-continuous boundary data. Making full use of the poly-Cauchy type integral operator in Clifford analysis, we give explicit integral expressions of solutions to this kind of boundary value problems over the sphere of \({\mathbb{R}^{n+1}}\) . As special cases solutions of the corresponding boundary value problems for the classical poly-analytic and meta-analytic functions are also derived, respectively.

Mathematics Subject Classification (2000)

30D10 30G35 32A25 58A10 

Keywords

Clifford analysis Riemann boundary value problems Generalized Cauchy–Riemann operator Poly-Cauchy type integral 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Center for Research and Development in Mathematics and ApplicationsUniversity of AveiroAveiroPortugal

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