A new approach to Cullen-regular functions of a quaternionic variable

Graziano Gentili; Daniele C. Struppa

doi:10.1016/j.crma.2006.03.015

Complex Analysis

A new approach to Cullen-regular functions of a quaternionic variable

Presented by: Jean-Pierre Demailly

Graziano Gentili ¹; Daniele C. Struppa ²

¹ Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67 A, Firenze, Italy
² Department of Mathematics and Computer Sciences, Chapman University, Orange, CA 92866, USA

Comptes Rendus. Mathématique, Volume 342 (2006) no. 10, pp. 741-744.

Abstract
Résumé

In this Note we announce the basic elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows an idea of Cullen, but we use a more geometric approach to show that it is possible to build a rather complete theory.

Dans ce travail nous annonçons les éléments et les résultats de base d'une nouvelle théorie des fonctions régulières d'une variable quaternionelle. La théorie que nous décrivons ici s'inspire d'une idée de Cullen, mais nous utilisons une approche plus géométrique pour montrer qu'il est possible de construire une théorie plutôt complète.

Received: 2005-12-01
Accepted: 2006-03-14
Published online: 2006-04-18

DOI: 10.1016/j.crma.2006.03.015

Author's affiliations:

Graziano Gentili ¹; Daniele C. Struppa ²

¹ Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67 A, Firenze, Italy
² Department of Mathematics and Computer Sciences, Chapman University, Orange, CA 92866, USA

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     author = {Graziano Gentili and Daniele C. Struppa},
     title = {A new approach to {Cullen-regular} functions of a quaternionic variable},
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     year = {2006},
     doi = {10.1016/j.crma.2006.03.015},
     language = {en},
}

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Graziano Gentili; Daniele C. Struppa. A new approach to Cullen-regular functions of a quaternionic variable. Comptes Rendus. Mathématique, Volume 342 (2006) no. 10, pp. 741-744. doi : 10.1016/j.crma.2006.03.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.03.015/

References
Cited by

[1] L. Ahlfors Complex Analysis, McGraw-Hill, New York, 1966

[2] F. Brackx; R. Delanghe; F. Sommen Clifford Analysis, Pitman Res. Notes in Math., vol. 76, 1982

[3] F. Colombo; I. Sabadini; F. Sommen; D.C. Struppa Analysis of Dirac Systems and Computational Algebra, Birkhäuser, 2004

[4] C.G. Cullen An integral theorem for analytic intrinsic functions on quaternions, Duke Math. J., Volume 32 (1965), pp. 139-148

[5] R. Fueter Die Funktionentheorie der Differentialgleichungen $Δ u = 0$ und $Δ Δ u = 0$ mit vier reellen Variablen, Comment. Math. Helv., Volume 7 (1934), pp. 307-330

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

[7] G. Gentili, D.C. Struppa, preprint, 2005

[8] G. Laville; I. Ramadanoff Holomorphic Cliffordian functions, Adv. Appl. Clifford Algebras, Volume 8 (1998), pp. 323-340

[9] G. Laville; I. Ramadanoff Elliptic Cliffordian functions, Complex Variables Theory Appl., Volume 45 (2001), pp. 297-318

[10] H. Leutwiler Modified quaternionic analysis in $R^{3}$ , Complex Variables Theory Appl., Volume 20 (1992), pp. 19-51

[11] R.F. Rinehart Elements of a theory of intrinsic functions on algebras, Duke Math. J., Volume 27 (1960), pp. 1-19

[12] A. Sudbery Quaternionic analysis, Math. Proc. Cambridge Philos. Soc., Volume 85 (1979), pp. 199-225

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