EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXIII, No. 31, pp. 115–136 (2006)

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

Claudia Garetto and G. H\"{o}rmann

Dipartimento di Matematica, Universita di Torino, Italia
Institut für Mathematik, Universität Wien, Austria

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.

Keywords: Colombeau generalized functions, duality theory, pseudodifferential operators, microlocal analysis

Classification (MSC2000): 46F30, 46A20, 47G30

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Electronic fulltext finalized on: 10 Jun 2006. This page was last modified: 20 Jun 2011.

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