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HAL CCSD Résumé : 15 pages
International audience
In analogy to the classical isomorphism between $mathcal{L}left( mathcal{S}left( mathbb{R}^{n}right) ,mathcal{S}^{prime}left( mathbb{R}^{m}right) right) $ and $mathcal{S}^{prime}left( mathbb{R}^{n+m}right) $, we show that a large class of moderate linear mappings acting between the space $mathcal{G}_{mathcal{S}}left( mathbb{R}^{n}right) $ of Colombeau rapidly decreasing generalized functions and the space $mathcal{G}_{ au}left( mathbb{R}^{n}right) $ of temperate ones admits generalized integral representations, with kernels belonging to $mathcal{G}_{ au}left( mathbb{R}^{n+m}right) $. Furthermore, this result contains the classical one in the sense of the generalized distribution equality.
Math. Proc. Camb. Philos. Soc.
Droits : info:eu-repo/semantics/OpenAccess
hal-00019916
https://hal.archives-ouvertes.fr/hal-00019916 https://hal.archives-ouvertes.fr/hal-00019916/document https://hal.archives-ouvertes.fr/hal-00019916/file/KernelSADelcroixfeb7th.pdf ARXIV : math.FA/0603035