Affiliations: Equipe Analyse Algébrique Non Linéaire, Laboratoire AOC, Faculté des sciences, Université des Antilles et de la Guyane, BP 250, 97157 Pointe à Pitre Cedex, Guadeloupe (France) | Equipe Analyse Algébrique Non Linéaire, Laboratoire GTSI, Faculté des sciences, Université des Antilles et de la Guyane, BP 250, 97157 Pointe à Pitre Cedex, Guadeloupe (France). Tel.: +590 (0) 590 48 30 84, Fax: +590 (0) 590 48 30 86; E-mail: [email protected] | Institute of Basic Sciences in Engineering, Unit of Engineering Mathematics, Faculty of Civil Engineering, University of Innsbruck, Technikerstraße 13, 6020 Innsbruck, Austria
Note: [] Corresponding author.
Note: [] Supported by FWF (Austria), Grant Y237.
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.
