Paley-Wiener Type Theorems for Colombeau′s Generalized Functions

We define the Laplace transformation for elements of Colombeau′s spaces Gc(Rn), G∞c(Rn) and Gt(Γ), where Γ is a cone. We obtain, in Theorems 1, 2, and 4, the "expected" Paley-Wiener type theorems for Gc(Rn) and Gt([0, ∞)). The Paley-Wiener type theorems are more complicated for elements of Gt(Γ), because the Laplace transformation depends on a cutoff function (Theorem 3).