Microlocal properties of basic operations in Colombeau algebras

The Colombeau algebra of generalized functions allows us to unrestrictedly carry out products of distributions. We analyze this operation from a micro local point of view, deriving a general inclusion relation for wave front s ets of products in the algebra. Furthermore, we give explicit examples show ing that the given result is optimal; i.e., its assumptions cannot be weake ned. Finally, we discuss the interrelation of these results with the concep t of pullback under smooth maps. (C) 2001 Academic Press.