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Advances in Applied Clifford Algebras

, Volume 22, Issue 2, pp 365–390 | Cite as

Riemann Boundary Value Problems on the Sphere in Clifford Analysis

  • Min KuEmail author
  • Uwe Kähler
  • Daoshun Wang
Article

Abstract

We present and study a type of Riemann boundary value problems (for short RBVPs) for polynomially monogenic functions, i.e. null solutions to polynomially generalized Cauchy-Riemann equations, over the sphere of \({\mathbb{R}^{n+1}}\). Making use of Fischer type decomposition and the Clifford calculus for polynomially monogenic functions, we obtain explicit expressions of solutions of this kind of boundary value problems over the sphere of \({\mathbb{R}^{n+1}}\). As special cases the solutions of the corresponding boundary value problems for classical polyanalytic functions and metaanalytic functions are derived respectively.

Keywords

Clifford analysis generalized Cauchy-Riemann operator Hölder continuous functions sphere Riemann boundary value problems 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Departamento de MatemáticaUniversidade de AveiroAveiroPortugal
  2. 2.Department of Computer Science and TechnologyTsinghua UniversityBeijingP.R. China

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