On subadditivity-like conditions for associated weight functions

TL;DR

This paper characterizes subadditivity-like growth conditions for associated weight functions using the defining weight sequence, which are crucial for properties like closedness under composition in ultradifferentiable function classes.

Contribution

It provides new characterizations of growth conditions for associated weight functions in terms of their defining sequences, enhancing understanding of ultradifferentiable function spaces.

Findings

Characterizations of subadditivity-like conditions in terms of weight sequences

Implications for ultradifferentiable function classes

Conditions related to closedness under composition

Abstract

The aim of this article is to provide characterizations for subadditivity-like growth conditions for the so-called associated weight functions in terms of the defning weight sequence. Such growth requirements arise frequently in the literature and are standard when dealing with ultradifferentiable function classes defned by Braun-Meise-Taylor weight functions since they imply or even characterize important and desired consequences for the underlying function spaces, e.g. closedness under composition.