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

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

2002-03-06

arxiv.org/abs/math/0203050v2

Trans. Amer. Math. Soc. 356 (2004), 4811-4827

Mathematics

Complex Variables

Final version : Corrected typographical errors, corrected proofs of lemmas 3.2 and 5.1; 16 pages

Scientific paper

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

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