Stratified Whitney jets and tempered ultradistributions on the subanalytic site

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Honda, N.
Morando, G.
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Abstract
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In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold X. Then we define stratified ultradistributions of Beurling and Roumieu type on X. In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if X is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to X. Second, the tempered-stratified ultradistributions on the complementary of a 1-regular closed subset of X coincide with the sections of the presheaf of tempered ultradistributions.
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Mathematics - Functional Analysis, Mathematics - Algebraic Geometry, 46M20 (Primary) 46F05, 32B20, 32C38 (Secondary)
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