Ultraholomorphic extension theorems in the mixed setting

TL;DR

This paper extends ultraholomorphic extension theorems to a mixed setting involving weight sequences and functions, introducing new growth indices and emphasizing the role of quasianalyticity for sectorial extensions.

Contribution

It generalizes existing ultraholomorphic extension theorems to a mixed framework, incorporating new growth indices and the order of quasianalyticity.

Findings

Established mixed ultraholomorphic extension theorems

Introduced new mixed growth indices

Highlighted the importance of quasianalyticity order

Abstract

The aim of this work is to generalize the ultraholomorphic extension theorems from V. Thilliez in the weight sequence setting and from the authors in the weight function setting (of Roumieu type) to a mixed framework. Such mixed results have already been known for ultradifferentiable classes and it seems natural that they have ultraholomorphic counterparts. In order to have control on the opening of the sectors in the Riemann surface of the logarithm for which the extension theorems are valid we are introducing new mixed growth indices which are generalizing the known ones for weight sequences and functions. As it turns out, for the validity of mixed extension results the so-called order of quasianalyticity (introduced by the second author for weight sequences) is becoming important.