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

2005/02/14 by Claudia Garetto, Garetto, Claudia
Mathematics · #35H05 #46F30 #47G30 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35H05 #msc:46F30 #msc:47G30

paper · pdf · doi:10.48550/arxiv.math/0502283

arxiv created 2005/02/14 · arxiv updated 2009/12/01

Abstract

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.

Related

• Perturbations of globally hypoelliptic pseudo-differential operators on ℝⁿ
• On partially hypoelliptic operators. Part II: Pseudo differential operators
• Global hypoellipticity for a class of overdetermined systems of pseudo-differential operators on the torus
• Pseudodifferentialoperatoren mit nichtglatten Koeffizienten auf Mannigfaltigkeiten
• Global symbolic calculus of pseudo-differential operators on homogeneous vector bundles