Revistes Catalanes amb Accés Obert (RACO)

Approximation par des fonctions holomorphes à croissance contrôlée

Ph. Charpentier, Y. Dupain, M. Mounkaila


Let $\Omega$ be a bounded pseuco-convex domain in $\Bbb C^n$ with a $\Cal C^{\infty}$ boundary, and let $S$ be the set of strictly pseudo-convex points of $\partial\Omega$. In this paper, we study the asymptotic behaviour of holomorphic functions along normals arising from points of $S$. We extend results obtained by M. Ortel and W. Schneider in the unit disc and those of A. Iordan and Y. Dupain in the unit ball of $\Bbb C^n$. We establish the existence of holomorphic functions of given growth having a "prescribed behaviour" on almost all normals arising from points of $S$.

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