On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets
2006 ◽
Vol 133
(31)
◽
pp. 115-136
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Keyword(s):
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 functional 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. AMS Mathematics Subject Classification (2000): 46F30, 46A20, 47G30.
2008 ◽
Vol 340
(2)
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pp. 1153-1170
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2006 ◽
Vol 58
(3)
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pp. 369-391
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1994 ◽
Vol 166
(1)
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pp. 263-271
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2016 ◽
Vol 111
(3)
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pp. 891-919
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2015 ◽
Vol 22
(5)
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pp. 1141-1156