Some Approximation Theorems of Weighted Bergman Space

Abstract:

Let H2(Ω,φ) be the Bergman space with respect to φ on the domain Ω. It is proved that holomorphic functions on Ω are dense in H2(Ω,φ) when Ω is the intersection of a finite number of Carathéodory domains and φ is a subharmonic function on Ω. If Ω = Cn and φ is approximately circular polynomials are dense in H2(Ω,φ).

Key words:Bergman space; Carathéodory domain; weighted L2 approximation; approximately circular