Stability properties of ultraholomorphic classes of Roumieu-type defined by weight matrices

TL;DR

This paper extends the understanding of stability properties of ultraholomorphic classes of Roumieu type, defined via weight matrices, by generalizing previous results to broader sectors and establishing new stability criteria.

Contribution

It generalizes known stability results from weight sequences to weight matrices and sectors of arbitrary opening, introducing characteristic functions for these classes.

Findings

Extended stability results to sectors on the Riemann surface of the logarithm.

Constructed characteristic functions for ultraholomorphic classes in unrestricted sectors.

Obtained new stability criteria using weight sequences and functions.

Abstract

We characterize several stability properties, such as inverse or composition closedness, for ultraholomorphic function classes of Roumieu type defined in terms of a weight matrix. In this way we transfer and extend known results from J. Siddiqi and M. Ider, from the weight sequence setting and in sectors not wider than a half-plane, to the weight matrix framework and for sectors in the Riemann surface of the logarithm with arbitrary opening. The key argument rests on the construction, under suitable hypotheses, of characteristic functions in these classes for unrestricted sectors. As a by-product, we obtain new stability results when the growth control in these classes is expressed in terms of a weight sequence, or of a weight function in the sense of Braun-Meise-Taylor.