Approximation par des fonctions holomorphes à croissance contrôlée

Autores: Philippe Charpentier, Yves Dupain, Modi Mounkaila
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 38, Nº 2, 1994, págs. 269-298
Idioma: francés
DOI: 10.5565/publmat_38294_02
Títulos paralelos:
- Aproximación por funciones holomorfas con crecimiento controlado
- Approximation through holomorphic functions of controlled growth
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Resumen
- 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 $S$.