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Étant donnés un compact du plan complexe, et une mesure non nulle sur , on étudie , l’adhérence dans , pour la topologie , de l’algèbre des fractions rationnelles d’une variable complexe, à pôles hors de . Le résultat principal obtenu est qu’il existe un sous-ensemble de , éventuellement vide, mesurable pour la mesure de Lebesgue plane, et une mesure , éventuellement nulle, absolument continue par rapport à la mesure , tels que : soit isométriquement isomorphe à , où désigne la...
For sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of the best -approximation with an unbounded number of finite poles are considered.
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