Geodesic
Fischer decompositions in Euclidean and Hermitean Clifford analysis
Archivum mathematicum, Tome 46 (2010) no. 5, pp. 301-321.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $\underline{\partial }$. 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 $\underline{\partial }_J$, leading to the system of equations $\underline{\partial } f = 0 = \underline{\partial }_J f$ 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.
Classification : 30G35
Keywords: Fischer decomposition; Clifford analysis 
@article{ARM_2010__46_5_a1,
     author = {Brackx, Fred and de Schepper, Hennie and Sou\v{c}ek, Vladim{\'\i}r},
     title = {Fischer decompositions in {Euclidean} and {Hermitean} {Clifford} analysis},
     journal = {Archivum mathematicum},
     pages = {301--321},
     publisher = {mathdoc},
     volume = {46},
     number = {5},
     year = {2010},
     mrnumber = {2753985},
     zbl = {1249.30135},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2010__46_5_a1/}
}
TY  - JOUR
AU  - Brackx, Fred
AU  - de Schepper, Hennie
AU  - Souček, Vladimír
TI  - Fischer decompositions in Euclidean and Hermitean Clifford analysis
JO  - Archivum mathematicum
PY  - 2010
SP  - 301
EP  - 321
VL  - 46
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ARM_2010__46_5_a1/
LA  - en
ID  - ARM_2010__46_5_a1
ER  - 
%0 Journal Article
%A Brackx, Fred
%A de Schepper, Hennie
%A Souček, Vladimír
%T Fischer decompositions in Euclidean and Hermitean Clifford analysis
%J Archivum mathematicum
%D 2010
%P 301-321
%V 46
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ARM_2010__46_5_a1/
%G en
%F ARM_2010__46_5_a1
Brackx, Fred; de Schepper, Hennie; Souček, Vladimír. Fischer decompositions in Euclidean and Hermitean Clifford analysis. Archivum mathematicum, Tome 46 (2010) no. 5, pp. 301-321. http://geodesic.mathdoc.fr/item/ARM_2010__46_5_a1/