Microlocal properties of basic operations in Colombeau algebras

Details Microlocal properties of basic operations in Colombeau algebras Microlocal properties of basic operations in Colombeau algebras

2000-08-28

arxiv.org/abs/math/0008206v1

J. Math. Anal. Appl. 261, 254-270, 2001.

Mathematics

Functional Analysis

LaTeX, 18 pages

Scientific paper

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.

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