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