English

Microlocal properties of basic operations in Colombeau algebras

Functional Analysis 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0008206,
  title  = {Microlocal properties of basic operations in Colombeau algebras},
  author = {Guenther Hoermann and Michael Kunzinger},
  journal= {arXiv preprint arXiv:math/0008206},
  year   = {2007}
}

Comments

LaTeX, 18 pages

R2 v1 2026-07-22T16:34:22.758Z