The linear invariants (DN) and (Ω) for spaces of germs of holomorphic functions on compact subsets of Cn

Abstract

For a compact subset K of Cn, we give necessary and sufficient conditions for [H(K)]′ to have the property (DN), and similarly for the property (Ω). We also show that H(D) is isomorphic to H(Δ n), where Δn is the unit polydisc in Cn and D is any bounded Reinhardt domain in Cn. This last result requires a generalization of the classical Hartogs phenomenon.