On the extension of Whitney ultrajets, II

TL;DR

This paper advances the understanding of Whitney extension theorems in ultradifferentiable function spaces by removing a key condition and clarifying open questions from prior work.

Contribution

It demonstrates that a specific condition in the main theorem can be omitted and addresses unresolved issues from previous research.

Findings

Condition (1.3) can be dropped from the main theorem.

Clarification of open questions in the ultradifferentiable Whitney extension theory.

Enhanced characterization of extension validity in the Roumieu setting.

Abstract

We characterize the validity of the Whitney extension theorem in the ultradifferentiable Roumieu setting with controlled loss of regularity. Specifically, we show that in the main Theorem 1.3 of [15] condition (1.3) can be dropped. Moreover, we clarify some questions that remained open in [15].