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<identifier>oai:HAL:hal-00020280v1</identifier>
<datestamp>2017-12-21</datestamp>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>Regular rapidly decreasing nonlinear generalized functions. Application to microlocal regularity</title>
<creator>Delcroix, Antoine</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>
<description>Submitted to the Journal of Mathematical Analysis and Applications</description>
<description>International audience</description>
<source>J. Math. Anal. Appl.</source>
<identifier>hal-00020280</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00020280</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00020280/document</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00020280/file/ADelcroixGRegularJan27.pdf</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00020280</source>
<source>J. Math. Anal. Appl., 2007, 327, pp.564-584. 〈10.1016/j.jmaa.2006.04.045〉</source>
<identifier>ARXIV : math/0603183</identifier>
<relation>info:eu-repo/semantics/altIdentifier/arxiv/math/0603183</relation>
<identifier>DOI : 10.1016/j.jmaa.2006.04.045</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2006.04.045</relation>
<language>en</language>
<subject lang=en>microlocal regularity</subject>
<subject lang=en>Colombeau generalized functions</subject>
<subject lang=en>rapidly decreasing generalized functions</subject>
<subject lang=en>Fourier transform</subject>
<subject>35A18, 35A27, 42B10, 46E10, 46F30</subject>
<subject>[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>We present new types of regularity for nonlinear generalized functions, based on the notion of regular growth with respect to the regularizing parameter of Colombeau's simplified model. This generalizes the notion of G^{ infty }-regularity introduced by M. Oberguggenberger. A key point is that these regularities can be characterized, for compactly supported generalized functions, by a property of their Fourier transform. This opens the door to microanalysis of singularities of generalized functions, with respect to these regularities. We present a complete study of this topic, including properties of the Fourier transform (exchange and regularity theorems) and relationship with classical theory, via suitable results of embeddings.</description>
<date>2007</date>
<rights>info:eu-repo/semantics/OpenAccess</rights>
</dc>
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