A new characterization of a class of pseudoconvex domains in $ {\mathbb{C}}^{2}$

Fabrizio Colombo; M. Elena Luna-Elizarrarás; Irene Sabadini; Michael Shapiro; Daniele C. Struppa

doi:10.1016/j.crma.2007.04.014

Complex Analysis

A new characterization of a class of pseudoconvex domains in

C^{2}

Presented by: Jean-Pierre Demailly

Fabrizio Colombo ¹; M. Elena Luna-Elizarrarás ²; Irene Sabadini ¹; Michael Shapiro ²; Daniele C. Struppa ³

¹ Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy
² Departamento de Matemáticas E.S.F.M. del I.P.N. 07338 México D.F., Mexico
³ Department of Mathematics and Computer Science, Chapman University, 92866 Orange, CA, USA

Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 677-680.

Abstract
Résumé

By using the right inverse of the Cauchy–Fueter operator we obtain an explicit integral characterization of a class of pseudoconvex domains in $C^{2}$ .

En utilisant l'inverse à droite de l'opérateur de Cauchy–Fueter, nous démontrons une caractérisation en forme intégrale d'une classe de domaines pseudoconvexes en $C^{2}$ .

Received: 2006-06-01
Accepted: 2007-04-03
Published online: 2007-05-23

DOI: 10.1016/j.crma.2007.04.014

Author's affiliations:

Fabrizio Colombo ¹; M. Elena Luna-Elizarrarás ²; Irene Sabadini ¹; Michael Shapiro ²; Daniele C. Struppa ³

¹ Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy
² Departamento de Matemáticas E.S.F.M. del I.P.N. 07338 México D.F., Mexico
³ Department of Mathematics and Computer Science, Chapman University, 92866 Orange, CA, USA

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     author = {Fabrizio Colombo and M. Elena Luna-Elizarrar\'as and Irene Sabadini and Michael Shapiro and Daniele C. Struppa},
     title = {A new characterization of a class of pseudoconvex domains in $ {\mathbb{C}}^{2}$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {677--680},
     publisher = {Elsevier},
     volume = {344},
     number = {11},
     year = {2007},
     doi = {10.1016/j.crma.2007.04.014},
     language = {en},
}

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Fabrizio Colombo; M. Elena Luna-Elizarrarás; Irene Sabadini; Michael Shapiro; Daniele C. Struppa. A new characterization of a class of pseudoconvex domains in $ {\mathbb{C}}^{2}$. Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 677-680. doi : 10.1016/j.crma.2007.04.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.04.014/

References
Cited by

[1] 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

[2] R. Fueter Über einen Hartogs'schen Satz, Comm. Math. Helv., Volume 12 (1939), pp. 75-80

[3] S. Krantz Function Theory of Several Complex Variables, John Wiley & Sons, New York, 1982

[4] I. Mitelman; M.V. Shapiro Differentiation of the Martinelli–Bochner integrals and the notion of hyperderivability, Math. Nachr., Volume 172 (1995), pp. 211-238

[5] K. Nôno Characterization of domains of holomorphy by the existence of hyper-conjugate harmonic functions, Rev. Roum. Math. Pures Appl., Volume 31 (1986), pp. 159-161

[6] J. Ryan Complex Clifford analysis and domains of holomorphy, J. Austral. Math. Soc. Ser. A, Volume 48 (1990), pp. 413-433

[7] M. Shapiro; N. Vasilevski On the Bergman kernel function in hypercomplex analysis, Acta Appl. Math., Volume 46 (1997), pp. 1-27

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