A Global Approximation Result by Bert Alan Taylor and the Strong Openness Conjecture in $${\mathbb {C}}^n$$ C n

Abstract

We improve a global approximation result by Bert Alan Taylor in \({\mathbb {C}}^n\) for holomorphic functions in weighted Hilbert spaces. The main tools are a variation of the theorem of Hormander on weighted \(L^2\)-estimates for the \({\overline{\partial }}\)-equation together with the solution of the strong openness conjecture. A counterexample to a global strong openness conjecture in \({\mathbb {C}}^n \) is also given here.