arXiv math/00082062000-08-28math.FA

Microlocal properties of basic operations in Colombeau algebras

Guenther Hoermann, Michael Kunzinger

备注：: LaTeX, 18 pages
发表信息：: J. Math. Anal. Appl. 261, 254-270, 2001.

英文摘要：

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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