On the extension of Whitney ultrajets

TL;DR

This paper establishes precise conditions under which Whitney's extension theorem holds in the ultradifferentiable Roumieu setting, accounting for controlled regularity loss.

Contribution

It provides necessary and sufficient criteria for Whitney's extension theorem in ultradifferentiable classes with regularity loss control.

Findings

Characterization of extension conditions in ultradifferentiable Roumieu classes

Necessary and sufficient criteria for Whitney extension in this setting

Extension theorem validity with controlled regularity loss

Abstract

We prove necessary and sufficient conditions for the validity of Whitney's extension theorem in the ultradifferentiable Roumieu setting with controlled loss of regularity.