Microlocal properties of basic operations in Colombeau algebras
نویسنده
چکیده
The Colombeau algebra of generalized functions allows to unrestrictedly carry out products of distributions. We analyze this operation from a microlocal point of view, deriving a general inclusion relation for wave front sets of products in the algebra. Furthermore, we give explicit examples showing that the given result is optimal, i.e. its assumptions cannot be weakened. Finally, we discuss the interrelation of these results with the concept of pullback under smooth maps. 2000 Mathematics Subject Classification. Primary 46F30, 35A21; Secondary 46F10, 35A27.
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