Microlocal Asymptotic Analysis in Algebras of Generalized Functions
Functional Analysis
2009-04-18 v1 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.0704.1077,
title = {Microlocal Asymptotic Analysis in Algebras of Generalized Functions},
author = {Antoine Delcroix and Michael Oberguggenberger and Jean-André Marti},
journal= {arXiv preprint arXiv:0704.1077},
year = {2009}
}
Comments
21 pages