Comptes Rendus
Analyse mathématique
Fonctions rationnelles et théorie de la réalisation: le cas hyper-analytique
Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 975-980.

Nous définissons et étudions l'anneau des fonctions rationnelles dans le cadre hyper-analytique. Nous donnons un nombre de définitions équivalentes de la rationalité. La multiplication de Cauchy–Kovalevskaya joue un rôle important dans la théorie.

We define and study the ring of rational functions in the hyperholomorphic setting. We give a number of equivalent characterizations of rationality. The Cauchy–Kovalevskaya product plays an important role in the arguments.

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DOI : 10.1016/S1631-073X(03)00233-4

Daniel Alpay 1 ; Baruch Schneider 1 ; Michael Shapiro 2 ; Dan Volok 1

1 Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israël
2 Departamento de Matemáticas, Escuela Superior de Fı́sica y Matemáticas, Instituto Politécnico Nacional, 07300 México, D.F., Mexique
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Daniel Alpay; Baruch Schneider; Michael Shapiro; Dan Volok. Fonctions rationnelles et théorie de la réalisation: le cas hyper-analytique. Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 975-980. doi : 10.1016/S1631-073X(03)00233-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00233-4/

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  • Daniel Alpay; Fabrizio Colombo; Kamal Diki; Irene Sabadini On a Polyanalytic Approach to Noncommutative de Branges–Rovnyak Spaces and Schur Analysis, Integral Equations and Operator Theory, Volume 93 (2021) no. 4 | DOI:10.1007/s00020-021-02649-1
  • Daniel Alpay; María E. Luna-Elizarrarás; Michael Shapiro; Daniele Struppa Gleason’s problem, rational functions and spaces of left-regular functions: The split-quaternion setting, Israel Journal of Mathematics, Volume 226 (2018) no. 1, p. 319 | DOI:10.1007/s11856-018-1696-y
  • Daniel Alpay; Fabrizio Colombo; Irene Sabadini Schur Analysis in the Quaternionic Setting: The Fueter Regular and the Slice Regular Case, Operator Theory (2015), p. 1745 | DOI:10.1007/978-3-0348-0667-1_20
  • Daniel Alpay; Fabrizio Colombo; Irene M. Sabadini Schur Analysis in the Quaternionic Setting: The Fueter Regular and the Slice Regular Case, Operator Theory (2014), p. 1 | DOI:10.1007/978-3-0348-0692-3_20-1
  • Daniel Alpay; David Levanony Rational Functions Associated with the White Noise Space and Related Topics, Potential Analysis, Volume 29 (2008) no. 2, p. 195 | DOI:10.1007/s11118-008-9094-4
  • D. Alpay; F. M. Correa-Romero; M. E. Luna-Elizarrarás; M. Shapiro Hyperholomorphic rational functions: the Clifford analysis case, Complex Variables and Elliptic Equations, Volume 52 (2007) no. 1, p. 59 | DOI:10.1080/17476930600793654
  • Daniel Alpay; Michael Shapiro; Dan Volok Reproducing Kernel Spaces of Series of Fueter Polynomials, Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems, Volume 162 (2006), p. 19 | DOI:10.1007/3-7643-7453-5_2
  • Daniel Alpay; Michael Shapiro; Dan Volok Rational hyperholomorphic functions in R4, Journal of Functional Analysis, Volume 221 (2005) no. 1, p. 122 | DOI:10.1016/j.jfa.2004.07.012

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