Holomorphic Approximation on Certain Weakly Pseudoconvex Domains in Cn

The purpose of this paper is to study the Mergelyan approximation property in L p and C k -scales on certain weakly pseudoconvex domains of finite/infinite type in C n . At the heart of our results lies the solvability of the additive Cousin problem with bounds as well as estimates of the ∂ ¯ -equation in the corresponding topologies.

Luzin-type Holomorphic Approximation on Closed Subsets of Open Riemann Surfaces

It is known that if E is a closed subset of an open Riemann surface R and f is a holomorphic function on a neighbourhood of E, then it is “usually” not possible to approximate f uniformly by functions holomorphic on all of R. We show, however, that for every open Riemann surface R and every closed subset E ⸦ R, there is closed subset F ⸦ E that approximates E extremely well, such that every function holomorphic on F can be approximated much better than uniformly by functions holomorphic on R.

Strong disk property for domains in open Riemann surfaces

We study the relation between the holomorphic approximation property and the strong disk property for an open set of an open Riemann surface or a Stein space of pure dimension 1.

Manifold-Valued Holomorphic Approximation

This note considers the problem of approximating continuous maps from sets in complex spaces into complex manifolds by holomorphic maps.