Generalized Hyperfunctions and Algebra of Megafunctions

Abstract

Sheaves of spaces of generalized hyperfunctions $\mathcal{B}\mathcal{G}$ and algebras of megafunctions $\mathcal{M}\mathcal{G}$ are introduced. The first one is a flabby sheaf. Moreover, there exist injective sheaf homomorphisms $\mathcal{G} \rightarrow \mathcal{B}\mathcal{G}$ and $\mathcal{B}\mathcal{G} \rightarrow \mathcal{M}\mathcal{G},$ where $\mathcal{G}$ is the algebra of Colombeau generalized functions.