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<identifier>oai:HAL:hal-00140656v1</identifier>
<datestamp>2017-12-21</datestamp>
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<publisher>HAL CCSD</publisher>
<title lang=en>Microlocal Asymptotic Analysis in Algebras of Generalized Functions</title>
<creator>Delcroix, Antoine</creator>
<creator>Marti, Jean-André</creator>
<creator>Oberguggenberger, Michael</creator>
<contributor>Centre de recherches et de ressources en éducation et formation (CRREF) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>Analyse Optimisation Controle (AOC) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>Groupe de Technologie des Surfaces et Interfaces (GTSI) ; Université des Antilles et de la Guyane (UAG) - Université des Antilles (Pôle Guadeloupe) ; Université des Antilles (UA) - Université des Antilles (UA)</contributor>
<contributor>Institute of Basic Sciences in Engineering (ISBE) ; Université d'Innsbruck</contributor>
<contributor>Michael Oberguggenberger is supported by FWF (Austria), grant Y237</contributor>
<description>21 pages Publié sous le titre: Spectral asymptotic analysis in algebras of generalized functions dans Asymptot. Anal. 59/1-2, 83-107, 2008.</description>
<description>International audience</description>
<source>Asymptot. Anal.</source>
<identifier>hal-00140656</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00140656</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00140656/document</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00140656/file/MicrolocalDelcroixMartiOberguggenbergerArkiv.pdf</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00140656</source>
<source>Asymptot. Anal., 2008, 59 (1-2), pp.83-107. 〈10.3233/ASY-2008-0885〉</source>
<identifier>ARXIV : 0704.1077</identifier>
<relation>info:eu-repo/semantics/altIdentifier/arxiv/0704.1077</relation>
<identifier>DOI : 10.3233/ASY-2008-0885</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.3233/ASY-2008-0885</relation>
<language>en</language>
<subject lang=en>microlocal analysis</subject>
<subject lang=en>generalized functions</subject>
<subject lang=en>nonlinear operators</subject>
<subject lang=en>presheaf</subject>
<subject lang=en>propagation of singularities</subject>
<subject lang=en>singular spectrum</subject>
<subject>35A18, 35A27, 46E10, 46F30, 46T30</subject>
<subject>[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA]</subject>
<subject>[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>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.</description>
<date>2008</date>
<rights>info:eu-repo/semantics/OpenAccess</rights>
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