Éditeur(s) : HAL CCSD
Résumé : International audience
Colloque en l'honneur de Robert Lutz.
Mulhouse, France

hal-01535440
https://hal.univ-antilles.fr/hal-01535440

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
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.
ISSN: 0022-247X

hal-01530748
https://hal.univ-antilles.fr/hal-01530748
https://hal.univ-antilles.fr/hal-01530748/document
https://hal.univ-antilles.fr/hal-01530748/file/delcroixgskttjan21.pdf
DOI : 10.1016/j.jmaa.2005.01.006

Éditeur(s) : HAL CCSD
Résumé : International audience
Generalized functions 2004
Novi Sad, Serbia

hal-01535462
https://hal.univ-antilles.fr/hal-01535462

Éditeur(s) : HAL CCSD Institute of Mathematics Polish Academy of Sciences
Résumé : International audience
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.
ISSN: 0137-6934

hal-01529541
https://hal.univ-antilles.fr/hal-01529541
https://hal.univ-antilles.fr/hal-01529541/document
https://hal.univ-antilles.fr/hal-01529541/file/delcroix.pdf
DOI : 10.4064/bc88-0-7

Éditeur(s) : 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