On the class of almost subadditive weight functions

Abstract

We answer a question from A. V. Abanin and P. T. Tien about so-called almost subadditive weight functions in the sense of Braun-Meise-Taylor. Using recent knowledge of a growth index for functions, crucially appearing in the ultraholomorphic setting, we are able to show the existence of weights such that there does not exist an equivalent almost subadditive function and hence almost subadditive weights are a proper subclass.

18 pages; minor stylistic changes, this version has been accepted for publication in J. Math. Anal. Appl

References in corpus (6)

• Composition in ultradifferentiable classes
• Sectorial extensions, via Laplace transforms, in ultraholomorphic classes defined by weight functions
• Indices of O-regular variation for weight functions and weight sequences
• Extension of Whitney jets of controlled growth
• On generalized definitions of ultradifferentiable classes
• On the regularization of sequences and associated weight functions