GARETTO, C., 2004. Pseudo-differential operators in algebras of generalized functions and global hypoellipticity. Acta Applicandae Mathematicae, 80 (2), pp. 123 - 174.
The aim of this work is to develop a global calculus for pseudo-differential operators acting on suitable algebras of generalized functions. In particular, a condition of global hypoellipticity of the symbols gives a result of regularity for the corresponding pseudo-differential equations. This calculus and this frame are proposed as tools for the study in Colombeau algebras of partial differential equations globally defined on ℝn.