Stratified Whitney jets and tempered ultradistributions on the subanalytic site

TL;DR

This paper introduces stratified Whitney jets and ultradistributions on the subanalytic site, establishing their properties and relations, especially on real surfaces and complements of certain subsets.

Contribution

It defines stratified Whitney jets and ultradistributions on the subanalytic site, and proves sheaf properties and equivalences for tempered ultradistributions in specific cases.

Findings

Tempered-stratified ultradistributions form a sheaf on real surfaces.

On the complement of a 1-regular closed subset, they coincide with sections of tempered ultradistributions.

The paper establishes foundational properties of these sheaves in subanalytic geometry.

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 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.