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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96431Let 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).Final version : Corrected typographical errors, corrected proofs of lemmas 3.2 and 5.1; 16 pagesComplex Variables32A38, 32F32 (primary); 32D99 (secondary)On peak-interpolation manifolds for A(Ω) for convex domains in C^ntext