Optimal embeddings of ultradistributions into differential algebras

TL;DR

This paper develops optimal embeddings of ultradistributions into differential algebras, enabling advanced microlocal analysis while addressing Schwartz-type impossibility constraints.

Contribution

It introduces a novel embedding framework for ultradistributions into differential algebras with optimal properties, extending microlocal analysis in these contexts.

Findings

Successful construction of ultradistribution embeddings into differential algebras.

Development of microlocal analysis compatible with ultradistribution spaces.

Resolution of Schwartz-type impossibility issues in this setting.

Abstract

We construct embeddings of spaces of non-quasianalytic ultradistributions into differential algebras enjoying optimal properties in view of a Schwartz type impossibility result, also shown in this article. We develop microlocal analysis in theses algebras consistent with the microlocal analysis in the corresponding spaces of ultradistributions.