On peak-interpolation manifolds for A(Ω) for convex domains in C^n

Gautam Bharali

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On peak-interpolation manifolds for A(Ω) for convex domains in C^n

Gautam Bharali

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Abstract

Let Ωbe a bounded, weakly convex domain in C^n, n>1, having real-analytic boundary. A(Ω) is the algebra of all functions holomorphic in Ωand continuous upto the boundary. A submanifold M\subset \partialΩis said to be complex-tangential if T_p(M) lies in the maximal complex subspace of T_p(\partialΩ) for each p \in M. We show that for real-analytic submanifolds M\subset \partialΩ, if M is complex-tangential, then every compact subset of M is a peak-interpolation set for A(Ω).

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Gautam Bharali. 2003-10-23. On peak-interpolation manifolds for A(Ω) for convex domains in C^n. https://arxiv.org/abs/math/0203050

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