Global representatives of Colombeau holomorphic generalized functions

Abstract

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 L Ω , is equal to zero. © Springer-Verlag 2007.