On peak-interpolation manifolds for A(\Omega) for convex domains in C^n
Complex Variables
2007-05-23 v2
Abstract
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).
Keywords
Cite
@article{arxiv.math/0203050,
title = {On peak-interpolation manifolds for A(\Omega) for convex domains in C^n},
author = {Gautam Bharali},
journal= {arXiv preprint arXiv:math/0203050},
year = {2007}
}
Comments
Final version : Corrected typographical errors, corrected proofs of lemmas 3.2 and 5.1; 16 pages