Ensembles pics pour $A^{\infty }\left(D\right)$

Chaumat, Jacques; Chollet, Anne-Marie

Annales de l'Institut Fourier, Tome 29 (1979) no. 3, pp. 171-200

Soit $D$ un domaine borné strictement pseudoconvexe dans ${\mathbf{C}}^n$ à frontière régulière $\partial D$. On montre que tout compact d’une sous-variété $N$ de $\partial D$ dont l’espace tangent $T_p\left(N\right)$ en chaque point $p$ de $N$ est contenu dans le sous-espace complexe maximal de $T_p\left(\partial D\right)$ est un ensemble pic pour $A^{\infty }\left(D\right)$, la classe des fonctions analytiques dans $D$ dont toutes les dérivées sont continues dans $\overline{D}$.

Let $D$ be a bounded strictly pseudoconvex domain in ${\mathbf{C}}^n$ with smooth boundary $\partial D$. Let $A^{\infty }\left(D\right)$ be the class of functions analytic in $D$ and continuous with all their derivatives in $\overline{D}$. Let $N$ be a $C^{\infty }$-submanifold of $\partial D$ whose tangent space $T_p\left(N\right)$ lies in the maximal complex subspace of $T_p\left(\partial D\right)$, for every $p\in N$. In this work, we show that every compact subset of $N$ is a peak set for $A^{\infty }\left(D\right)$.

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