Pseudo-differential operators in algebras of generalized functions and global hypoellipticity Claudia Garetto 2134/17303 https://repository.lboro.ac.uk/articles/journal_contribution/Pseudo-differential_operators_in_algebras_of_generalized_functions_and_global_hypoellipticity/9385124 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. 2015-04-17 14:53:01 Colombeau algebras Global hypoellipticity Pseudo-differential operators Mathematical Sciences not elsewhere classified