Complex Analysis and Operator Theory

, Volume 6, Issue 2, pp 425–446 | Cite as

The Monogenic Fischer Decomposition: Two Vector Variables

  • P. Van LanckerEmail author


In this paper we will present two proofs of the monogenic Fischer decomposition in two vector variables. The first one is based on the so-called “Harmonic Separation of Variables Theorem” while the second one relies on some simple dimension arguments. We also show that these decomposition are still valid under milder assumptions than the usual stable range condition. In the process, we derive explicit formula for the summands in the monogenic Fischer decomposition of harmonics.


Clifford analysis Dirac operators Representations Fischer decomposition Spin groups 

Mathematics Subject Classification (2000)

30G35 42B37 35J05 


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© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Engineering Sciences, Member of Ghent University AssociationUniversity College GhentGhentBelgium

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