Analyse mathématique
Fonctions rationnelles et théorie de la réalisation: le cas hyper-analytique
[Rational functions and realization theory: the hyperholomorphic case]
Comptes Rendus. Mathématique, Volume 336 (2003) no. 12, pp. 975-980.

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.

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.

Published online:
DOI: 10.1016/S1631-073X(03)00233-4
Alpay, Daniel 1; Schneider, Baruch 1; Shapiro, Michael 2; Volok, Dan 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
     author = {Alpay, Daniel and Schneider, Baruch and Shapiro, Michael and Volok, Dan},
     title = {Fonctions rationnelles et th\'eorie de la r\'ealisation: le cas hyper-analytique},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {975--980},
     publisher = {Elsevier},
     volume = {336},
     number = {12},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00233-4},
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Alpay, Daniel; Schneider, Baruch; Shapiro, Michael; Volok, Dan. 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.

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