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On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006), p. 115
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Summarizing basic facts from abstract topological modules over Co\-lom\-be\-au 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.
DOI : 10.2298/BMAT0631115G
Classification : 46F30 46A20 47G30
Keywords: Colombeau generalized functions, duality theory, pseudodifferential operators, microlocal analysis 
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     author = {Claudia Garetto and G. Hormann},
     title = {On duality theory and pseudodifferential techniques for {Colombeau} algebras: generalized delta functionals, kernels and wave front sets},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {115 },
     year = {2006},
     volume = {31},
     doi = {10.2298/BMAT0631115G},
     zbl = {1121.46037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/BMAT0631115G/}
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Claudia Garetto; G. Hormann. On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006), p. 115 . doi: 10.2298/BMAT0631115G

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