On peak-interpolation manifolds for A() for convex domains in Cn
Abstract
Let be a bounded, weakly convex domain in Cn, n>1, having real-analytic boundary. A() is the algebra of all functions holomorphic in and continuous upto the boundary. A submanifold M⊂ ∂ is said to be complex-tangential if Tp(M) lies in the maximal complex subspace of Tp(∂) for each p ∈ M. We show that for real-analytic submanifolds M⊂ ∂, if M is complex-tangential, then every compact subset of M is a peak-interpolation set for A().
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