On the extension of Whitney ultrajets of Beurling type

TL;DR

This paper extends Whitney's theorem to ultradifferentiable Beurling classes, establishing the existence of continuous linear extension operators for Whitney ultrajets on arbitrary closed sets in Euclidean space.

Contribution

It introduces a Beurling-type extension theorem with controlled regularity loss and constructs continuous linear extension operators for Whitney ultrajets.

Findings

Extension theorem in Beurling ultradifferentiable setting

Existence of continuous linear extension operators

Controlled loss of regularity in extensions

Abstract

We prove a version of Whitney's extension theorem in the ultradifferentiable Beurling setting with controlled loss of regularity. As a by-product we show the existence of continuous linear extension operators on certain spaces of Whitney ultrajets on arbitrary closed sets in $\mathbb R^n$.