HOLOMORPHIC APPROXIMATION AND MIXED BOUNDARY VALUE PROBLEMS FOR ∂
Résumé
In this paper we study holomorphic approximation using boundary value problems for $\overline\partial$ on an annulus in the Hilbert space setting. The associated boundary conditions for $\overline\partial$ are the mixed boundary problems on an annulus. We characterize pseudoconvexity and Runge type property of the domain by the vanishing of related $L^2$ cohomology groups.
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