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Soit , un domaine borné, strictement pseudo-convexe de , on note , la classe des fonctions analytiques dans , continues ainsi que toutes leurs dérivées dans . Le principal résultat de ce travail est une condition suffisante pour qu’un sous-ensemble fermé de la frontière de soit l’ensemble des zéros d’une fonction de et aussi l’ensemble des zéros communs à et à toutes ses dérivées.
Soit un domaine borné strictement pseudoconvexe dans à frontière régulière . On montre que tout compact d’une sous-variété de dont l’espace tangent en chaque point de est contenu dans le sous-espace complexe maximal de est un ensemble pic pour , la classe des fonctions analytiques dans dont toutes les dérivées sont continues dans .
In this paper we obtain some equivalent characterizations of Bloch functions on general bounded strongly pseudoconvex domains with smooth boundary, which extends the known results in [1, 9, 10].
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