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