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Bulletin de la SMF - Parutions - 139 (2011) 389-435

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Stratified Whitney jets and tempered ultradistributions on the subanalytic site
N. Honda, G. Morando
Bulletin de la SMF 139, fascicule 3 (2011), 389-435

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Résumé :
Jets stratifiés de Whitney et ultradistributions tempérées sur le site sous-analytique
Dans cet article nous introduisons le faisceau des jets de Whitney d'ordre de Gevrey sur le site sous-analytique relatif à une variété analytique réelle . Ensuite, nous définissons les ultradistributions tempérées sur de type Beurling et Roumieu. Enfin, à travers les ultradistributions stratifiées, nous définissons les ultradistributions tempérées-stratifiées et nous démontrons les deux résultats suivants : (a) si est une surface réelle, les ultradistributions tempérées-stratifiées définissent un faisceau sur le site sous-analytique relatif à , et (b) les ultradistributions tempérées-stratifiées sur le complémentaire d'un sous-ensemble fermé -régulier de , coïncident avec les sections du préfaisceau des ultradistributions tempérées.

Mots-clefs : Faisceaux sur des sites sous-analytiques, ultradistributions tempérées, jets de Whitney

Abstract:
In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold . Then, we define stratified ultradistributions of Beurling and Roumieu type on . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to . Second, the tempered-stratified ultradistributions on the complementary of a -regular closed subset of coincide with the sections of the presheaf of tempered ultradistributions.

Keywords: Sheaves on subanalytic sites, tempered ultradistributions, Whitney jets

Class. math. : 46M20; 46F05 32B20 32C38

ISSN : 0037-9484
Publié avec le concours de : Centre National de la Recherche Scientifique

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