Equality of ultradifferentiable classes by means of indices of mixed O-regular variation

TL;DR

This paper introduces new growth indices based on O-regular variation to compare ultradifferentiable function classes defined by weight matrices and associated functions, extending existing comparison results.

Contribution

It develops a novel framework using mixed O-regular variation indices to characterize equality of ultradifferentiable classes from weight matrices and functions.

Findings

New growth indices extend O-regular variation to mixed settings

Characterization of class equality via these indices

Extension of comparison results between weight sequences and functions

Abstract

We characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These indices, defined by means of weight sequences and (associated) weight functions, are extending the notion of O-regular variation to a mixed setting. Hence we are extending the known comparison results concerning classes defined in terms of a single weight sequence and of a single weight function and give also these statements an interpretation expressed in O-regular variation.