Advances in Applied Clifford Algebras

, Volume 22, Issue 3, pp 563–575 | Cite as

A Goursat Decomposition for Polyharmonic Functions in Euclidean Space

  • Fred Brackx
  • Richard Delanghe
  • Hennie De Schepper
  • Vladimir Souček


The Goursat representation formula in the complex plane, expressing a real-valued biharmonic function in terms of two holomorphic functions and their anti-holomorphic complex conjugates, is generalized to Euclidean space, expressing a real-valued polyharmonic function of order p in terms of p the so called monogenic functions of Clifford analysis.

Mathematics Subject Classification (2010)



Goursat decomposition polyharmonic function 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Fred Brackx
    • 1
  • Richard Delanghe
    • 1
  • Hennie De Schepper
    • 1
  • Vladimir Souček
    • 2
  1. 1.Clifford Research Group, Faculty of Engineering and ArchitectureGhent UniversityGentBelgium
  2. 2.Mathematical Institute, Faculty of Mathematics and PhysicsCharles University PraguePragueCzech Republic

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