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<identifier>oai:HAL:hal-01529541v1</identifier>
<datestamp>2017-12-21</datestamp>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>Kernel theorems in spaces of generalized functions</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>International audience</description>
<source>ISSN: 0137-6934</source>
<source>EISSN: 1730-6299</source>
<source>Banach Center Publications</source>
<publisher>Institute of Mathematics Polish Academy of Sciences</publisher>
<identifier>hal-01529541</identifier>
<identifier>https://hal.univ-antilles.fr/hal-01529541</identifier>
<identifier>https://hal.univ-antilles.fr/hal-01529541/document</identifier>
<identifier>https://hal.univ-antilles.fr/hal-01529541/file/delcroix.pdf</identifier>
<source>https://hal.univ-antilles.fr/hal-01529541</source>
<source>Banach Center Publications, Institute of Mathematics Polish Academy of Sciences, 2010, 88, pp.77-89. 〈10.4064/bc88-0-7〉</source>
<identifier>DOI : 10.4064/bc88-0-7</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.4064/bc88-0-7</relation>
<language>en</language>
<subject lang=en>Compatctly supported generalized functions</subject>
<subject lang=en>Kernel theorems</subject>
<subject lang=en> generalized functions</subject>
<subject lang=en> Colombeau</subject>
<subject lang=en> Rapidly decreasing generalized functions</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>In analogy to the classical isomorphism between L(D(Rn);D0(Rm)) and D0(Rm+n) (resp. L(S(Rn); S0(Rm)) and S0(Rm+n)), we show that a large class of moderate linear mappings acting between the space GC(Rn) of compactly supported generalized functions and G(Rn) of generalized functions (resp. the space GS(Rn) of Colombeau rapidly decreasing generalized functions and the space G (Rn) of temperate ones) admits generalized integral representations, with kernels belonging to specic regular subspaces of G(Rm+n) (resp. G (Rm+n)). The main novelty is to use accelerated -nets, which are unit elements for the convolution product in these regular subspaces, to construct the kernels. Finally, we establish a strong relationship between these results and the classical ones.</description>
<date>2010</date>
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