Complex Analysis
Algebraic analysis of Hermitian monogenic functions
Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 139-142.

In this Note we present an algebraic analysis of the system of differential equations described by the Hermitian Dirac operators, which are two linear first order operators invariant with respect to the action of the unitary group, both in the case of one and several variables.

Nous présentons l'analyse algébrique du système associé aux opérateurs de Dirac Hermitiens. Ceux-ci sont deux opérateurs linéaires du premier ordre, invariant sous l'action du groupe unitaire. Nous étudions le cas d'une et des plusieurs variables.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2007.12.009
Damiano, Alberto 1; Eelbode, David 2; Sabadini, Irene 3

1 Mathematics Department, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
2 Department of Mathematical Analysis, Clifford Research Group, Ghent University, Galglaan 2, B-9000 Ghent, Belgium
3 Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy
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Damiano, Alberto; Eelbode, David; Sabadini, Irene. Algebraic analysis of Hermitian monogenic functions. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 139-142. doi : 10.1016/j.crma.2007.12.009. http://www.numdam.org/articles/10.1016/j.crma.2007.12.009/

[1] Brackx, F.; Bureš, J.; De Schepper, H.; Eelbode, D.; Sommen, F.; Souček, V. Fundaments of Hermitian Clifford analysis – Part I: Complex structure, Complex Anal. Oper. Theory, Volume 1 (2007) no. 3, pp. 341-365

[2] F. Brackx, J. Bureš, H. De Schepper, D. Eelbode, F. Sommen, V. Souček, Fundaments of Hermitian Clifford analysis – Part II: Splitting of h-monogenic equations, Compl. Var. Ell. Equa., in press

[3] Colombo, F.; Sabadini, I.; Sommen, F.; Struppa, D.C. Analysis of Dirac Systems and Computational Algebra, Progress in Mathematical Physics, vol. 39, Birkhäuser, Boston, 2004

[4] A. Damiano, D. Eelbode, I. Sabadini, Invariant syzygies for the Hermitian Dirac operator, preprint, 2007

[5] A. Damiano, D. Eelbode, I. Sabadini, Quaternionic Hermitian spinor systems and compatibility conditions, in preparation

[6] D. Eelbode, Quaternionic monogenic function systems, preprint, 2007

[7] Peña-Peña, D.; Sabadini, I.; Sommen, F. Quaternionic Clifford analysis: The Hermitian setting, Complex Anal. Oper. Theory, Volume 1 (2007) no. 1, pp. 97-113

[8] Sabadini, I.; Sommen, F. Hermitian Clifford analysis and resolutions, Math. Methods Appl. Sci., Volume 25 (2002) no. 16–18, pp. 1395-1413

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