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Microlocal Properties of Basic Operations in Colombeau Algebras

✍ Scribed by Günther Hörmann; Michael Kunzinger

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
152 KB
Volume
261
Category
Article
ISSN
0022-247X

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✦ Synopsis

The Colombeau algebra of generalized functions allows us 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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