On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets

2005/07/11 by Claudia Garetto, Garetto, Claudia, Guenther Hoermann +1
Mathematics · #13J99 #35D10 #35S30 #46F30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA #msc:13J99 #msc:35D10 #msc:35S30 #msc:46F30

paper · pdf · doi:10.48550/arxiv.math/0507222

arxiv created 2005/07/12 · arxiv updated 2009/12/01

Abstract

Summarizing basic facts from abstract topological modules over Colombeau generalized complex numbers we discuss duality of Colombeau algebras. In particular, we focus on generalized delta functionals and operator kernels as elements of dual spaces. A large class of examples is provided by pseudodifferential operators acting on Colombeau algebras. By a refinement of symbol calculus we review a new characterization of the wave front set for generalized functions with applications to microlocal analysis.

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