Algebraic analysis of Hermitian monogenic functions

Alberto Damiano; David Eelbode; Irene Sabadini

doi:10.1016/j.crma.2007.12.009

Complex Analysis

Algebraic analysis of Hermitian monogenic functions

Presented by: Jean-Pierre Demailly

Alberto Damiano ¹; David Eelbode ²; Irene Sabadini 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

Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 139-142.

Abstract
Résumé

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.

Received: 2007-09-23
Accepted: 2007-12-12
Published online: 2008-01-14

DOI: 10.1016/j.crma.2007.12.009

Author's affiliations:

Alberto Damiano ¹; David Eelbode ²; Irene Sabadini 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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     author = {Alberto Damiano and David Eelbode and Irene Sabadini},
     title = {Algebraic analysis of {Hermitian} monogenic functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {139--142},
     publisher = {Elsevier},
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     year = {2008},
     doi = {10.1016/j.crma.2007.12.009},
     language = {en},
}

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Alberto Damiano; David Eelbode; Irene Sabadini. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.12.009/

References
Cited by

[1] F. Brackx; J. Bureš; H. De Schepper; D. Eelbode; F. Sommen; V. Souček 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] F. Colombo; I. Sabadini; F. Sommen; D.C. Struppa 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] D. Peña-Peña; I. Sabadini; F. Sommen Quaternionic Clifford analysis: The Hermitian setting, Complex Anal. Oper. Theory, Volume 1 (2007) no. 1, pp. 97-113

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

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