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On peak-interpolation manifolds for

Authors:	Gautam Bharali

Institution:	Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706

Abstract:	Let $\Omega$ be a bounded, weakly convex domain in ${\mathbb{C} }^n$ , $n\geq 2$ , having real-analytic boundary. $A(\Omega)$ is the algebra of all functions holomorphic in $\Omega$ and continuous up to the boundary. A submanifold $\boldsymbol{M}\subset \partial \Omega$ is said to be complex-tangential if $T_p(\boldsymbol{M})$ lies in the maximal complex subspace of $T_p(\partial \Omega)$ for each $p\in\boldsymbol{M}$ . We show that for real-analytic submanifolds $\boldsymbol{M}\subset\partial \Omega$ , if $\boldsymbol{M}$ is complex-tangential, then every compact subset of $\boldsymbol{M}$ is a peak-interpolation set for $A(\Omega)$ .

Keywords:	Complex-tangential finite type domain interpolation set pseudoconvex domain

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