Microlocal Asymptotic Analysis in Algebras of Generalized Functions

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dc.creatorDelcroix, Antoine
dc.creatorOberguggenberger, Michael
dc.creatorMarti, Jean-André
dc.date2007-04-09
dc.date.accessioned2026-07-07T13:05:16Z
dc.date.available2026-07-07T13:05:16Z
dc.descriptionWe 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.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/0704.1077
dc.identifierhttp://arxiv.org/abs/0704.1077
dc.identifierAsymptot. Anal. 59, 1-2 (2008) 83-107
dc.identifierdoi:10.3233/ASY-2008-0885
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227438
dc.subjectFunctional Analysis
dc.subjectAnalysis of PDEs
dc.subject35A18, 35A27, 46E10, 46F30, 46T30
dc.titleMicrolocal Asymptotic Analysis in Algebras of Generalized Functions
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