Sectorial extensions for ultraholomorphic classes defined by weight functions

TL;DR

This paper extends ultraholomorphic classes defined by Braun-Meise-Taylor weight functions, using real methods and Whitney-extension theorem, to establish sectorial extension theorems for both Roumieu and Beurling cases.

Contribution

It introduces a new approach for sectorial extension theorems in ultraholomorphic classes using weight functions, differing from previous sequence-based methods.

Findings

Proved an extension theorem for ultraholomorphic classes with weight functions.

Transferred proofs from sequence to weight function setting.

Handled both Roumieu and Beurling cases through reduction.

Abstract

We prove an extension theorem for ultraholomorphic classes defined by so-called Braun-Meise-Taylor weight functions and transfer the proofs from the single weight sequence case from V. Thilliez [28] to the weight function setting. We are following a different approach than the results obtained in [11], more precisely we are working with real methods by applying the ultradifferentiable Whitney-extension theorem. We are treating both the Roumieu and the Beurling case, the latter one is obtained by a reduction from the Roumieu case.