Global Representatives of Colombeau Holomorphic Generalized Functions

It is proved that a holomorphic generalized function in the sense of Colombeau has a representative consisting of a net of holomorphic functions. More generally, the existence of global representatives of Colombeau solutions to elliptic partial differential equations is proved. Further, it is shown that a generalized holomorphic function on Ω, which is equal to zero in an open set , is equal to zero. First author partially supported by FWF (Austria), grants P16820 and Y237. Third author partially supported by MNZŽ (Serbia), project 144016.