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<identifier>oai:HAL:hal-01530748v1</identifier>
<datestamp>2017-12-21</datestamp>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>Generalized Integral Operators and Schwartz Kernel Theorem</title>
<creator>Delcroix, Antoine</creator>
<contributor>Analyse Optimisation Controle (AOC) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>Centre de recherches et de ressources en éducation et formation (CRREF) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>ISSN: 0022-247X</source>
<source>Journal of Mathematical Analysis and Applications</source>
<publisher>Elsevier</publisher>
<identifier>hal-01530748</identifier>
<identifier>https://hal.univ-antilles.fr/hal-01530748</identifier>
<identifier>https://hal.univ-antilles.fr/hal-01530748/document</identifier>
<identifier>https://hal.univ-antilles.fr/hal-01530748/file/delcroixgskttjan21.pdf</identifier>
<source>https://hal.univ-antilles.fr/hal-01530748</source>
<source>Journal of Mathematical Analysis and Applications, Elsevier, 2005, 306 (2), pp.481-501. 〈https://ees.elsevier.com/jmaa/〉. 〈10.1016/j.jmaa.2005.01.006〉</source>
<identifier>DOI : 10.1016/j.jmaa.2005.01.006</identifier>
<relation>info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2005.01.006</relation>
<source>https://ees.elsevier.com/jmaa/</source>
<language>en</language>
<subject lang=en>Schwartz kernel theorem</subject>
<subject lang=en> Colombeau nonlinear generalized functions</subject>
<subject lang=en> Integral operator</subject>
<subject lang=en> distributions</subject>
<subject>2000 MSC: 45P05, 46F05, 46F30, 47G10</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 Schwartz kernel theorem, we show that a large class of linear mappings admits integral kernels in the framework of Colombeau generalized functions. To do this, we introduce new spaces of generalized functions with slow growth and the corresponding adapted linear mappings. Finally, we show that, in some sense, Schwartz’ result is contained in our main theorem.</description>
<date>2005</date>
</dc>
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