Generalized Analytic Functions on Generalized Domains

We define the algebra G̃(A) of Colombeau generalized functions on a subset A of the space of generalized points R̃d. If A is an open subset of R̃d, such generalized functions can be identified with pointwise maps from A into the ring of generalized numbers C̃. We study analyticity in G̃(A), where A is an open subset of C̃. In particular, if the domain is an open ball for the sharp norm on C̃, we characterize analyticity and give a unicity theorem involving the values at generalized points.