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
[L'analyse algébrique des fonctions monogènes Hermitiennes]

Présenté par : 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 (VO)
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.

Reçu le : 2007-09-23
Accepté le : 2007-12-12
Publié le : 2008-01-14

DOI : 10.1016/j.crma.2007.12.009

Affiliations des auteurs :

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},
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     pages = {139--142},
     publisher = {Elsevier},
     volume = {346},
     number = {3-4},
     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/

Bibliographie
Cité par

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Ricardo Abreu-Blaya; Juan Bory-Reyes; Fred Brackx; Hennie De Schepper; Tania Moreno-García; Frank Sommen Boundary value problems on fractal hypersurfaces for the quaternionic Hermitian system in ${{\mathbb}} {R}^{4n}$ , Complex Analysis and Operator Theory, Volume 9 (2015) no. 5, pp. 957-973 | DOI:10.1007/s11785-014-0370-6 | Zbl:1317.30072
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Irene Sabadini; Frank Sommen Hermitian Clifford Analysis, Operator Theory (2015), p. 1581 | DOI:10.1007/978-3-0348-0667-1_13
Guangbin Ren; Haiyan Wang; Lin Chen Paracomplex Hermitean Clifford analysis, Complex Analysis and Operator Theory, Volume 8 (2014) no. 6, pp. 1367-1382 | DOI:10.1007/s11785-013-0341-3 | Zbl:1306.30021
Irene M. Sabadini; Frank Sommen Hermitian Clifford Analysis, Operator Theory (2014), p. 1 | DOI:10.1007/978-3-0348-0692-3_13-1
Guangbin Ren; Haiyan Wang Theory of several paravector variables: Bochner-Martinelli formula and Hartogs theorem, Science China. Mathematics, Volume 57 (2014) no. 11, pp. 2347-2360 | DOI:10.1007/s11425-014-4878-z | Zbl:1304.30067
Ricardo Abreu-Blaya; Juan Bory-Reyes; Fred Brackx; Hennie De Schepper; Frank Sommen Matrix Cauchy and Hilbert transforms in Hermitian quaternionic Clifford analysis, Complex Variables and Elliptic Equations, Volume 58 (2013) no. 8, pp. 1057-1069 | DOI:10.1080/17476933.2011.626034 | Zbl:1318.30073
Ricardo Abreu-Blaya; Juan Bory-Reyes; Fred Brackx; Hennie De Schepper; Frank Sommen Boundary value problems for the quaternionic Hermitian system in ${{\mathbb}} {R}^{4n}$ , Boundary Value Problems, Volume 2012 (2012), p. 13 (Id/No 74) | DOI:10.1186/1687-2770-2012-74 | Zbl:1276.30058
Ricardo Abreu-Blaya; Juan Bory-Reyes; Fred Brackx; Hennie De Schepper; Frank Sommen Cauchy integral formulae in quaternionic Hermitean Clifford analysis, Complex Analysis and Operator Theory, Volume 6 (2012) no. 5, pp. 971-985 | DOI:10.1007/s11785-011-0168-8 | Zbl:1275.30017
Alberto Damiano; David Eelbode; Irene Sabadini Quaternionic Hermitian spinor systems and compatibility conditions, Advances in Geometry, Volume 11 (2011) no. 1, pp. 169-189 | DOI:10.1515/advgeom.2010.045 | Zbl:1235.30030
Alberto Damiano; David Eelbode; Irene Sabadini Invariant syzygies for the Hermitian Dirac operator, Mathematische Zeitschrift, Volume 262 (2009) no. 4, pp. 929-945 | DOI:10.1007/s00209-008-0414-6 | Zbl:1175.58014

Cité par 11 documents. Sources : Crossref, zbMATH

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