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Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna
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Approximation of holomorphic mappings on strongly pseudoconvex domains
Let D be a relatively compact strongly pseudoconvex domain in a Stein manifold S. We prove that for every complex manifold Y the set 𝒜(D, Y) of all continuous maps → Y which are holomorphic in D is a complex Banach manifold, and every ƒ ∈ 𝒜(D, Y) can be approximated uniformly on by maps holomorphic in open neighborhoods of in S. Analogous results are obtained for maps of class 𝒜r(D), r ∈ . We also establish the Oka property for sections of continuous or smooth fiber bundles over which are holomorphic over D and whose fiber enjoys the Convex Approximation Property (Theorem 1.7).
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