Pseudo-differential operators in algebras of generalized functions and global hypoellipticity

Details Pseudo-differential operators in algebras of generalized functions and global hypoellipticity Pseudo-differential operators in algebras of generalized functions and global hypoellipticity

2005-02-14

arxiv.org/abs/math/0502283v1

Mathematics

Analysis of PDEs

Scientific paper

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 $\mathbb{R}^n$.

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