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On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets
journal contribution
posted on 2015-04-20, 10:11 authored by Claudia Garetto, Gunther HormannSummarizing 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.
Funding
GH was supported by FWF grant P16820-N04
History
School
- Science
Department
- Mathematical Sciences