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(2010)ARCHIVUM MATHEMATICUM.46(5).p.301-321 Mark abstract Euclidean Clifford analysis is a higher dimensional function theory studying so--called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator D. In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator D_J, leading to the system of equations D f = 0 = D_J f expressing so-called Hermitean monogenicity. The invariance of this system is reduced to the unitary group U(n). In this paper we decompose the spaces of homogeneous monogenic polynomials into U(n)-irrucibles involving homogeneous Hermitean monogenic polynomials and we carry out a dimensional analysis of those spaces. Meanwhile an overview is given of so-called Fischer decompositions in Euclidean and Hermitean Clifford analysis.

Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-1099690



Autor: Fred Brackx , Hennie De Schepper and Vladímir Souček

Fuente: https://biblio.ugent.be/publication/1099690



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