Microlocal Asymptotic Analysis in Algebras of Generalized Functions

Details Microlocal Asymptotic Analysis in Algebras of Generalized Functions Microlocal Asymptotic Analysis in Algebras of Generalized Functions

2007-04-09

arxiv.org/abs/0704.1077v1

Asymptot. Anal. 59, 1-2 (2008) 83-107

Mathematics

Functional Analysis

21 pages

Scientific paper

10.3233/ASY-2008-0885

We introduce a new type of local and microlocal asymptotic analysis in algebras of generalized functions, based on the presheaf properties of those algebras and on the properties of their elements with respect to a regularizing parameter. Contrary to the more classical frequential analysis based on the Fourier transform, we can describe a singular asymptotic spectrum which has good properties with respect to nonlinear operations. In this spirit we give several examples of propagation of singularities through nonlinear operators.

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