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 $\mathbb{R}^n$.
Microlocal analysis of generalized functions: pseudodifferential techniques and propagation of singularities
Global hypoellipticity for a class of overdetermined systems of pseudo-differential operators on the torus
Existence of mild solutions for a system of partial differential equations with time-dependent generators
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