Nonlinear conditions for ultradifferentiability
Classical Analysis and ODEs
2022-12-29 v2 Complex Variables
Functional Analysis
Abstract
A remarkable theorem of Joris states that a function is if two relatively prime powers of are . Recently, Thilliez showed that an analogous theorem holds in Denjoy--Carleman classes of Roumieu type. We prove that a division property, equivalent to Joris's result, is valid in a wide variety of ultradifferentiable classes. Generally speaking, it holds in all dimensions for non-quasianalytic classes. In the quasianalytic case we have general validity in dimension one, but we also get validity in all dimensions for certain quasianalytic classes.
Cite
@article{arxiv.2102.03871,
title = {Nonlinear conditions for ultradifferentiability},
author = {David Nicolas Nenning and Armin Rainer and Gerhard Schindl},
journal= {arXiv preprint arXiv:2102.03871},
year = {2022}
}
Comments
21 pages; Version 2: The division property in the first version is equivalent to property (2) in the current version. This simplifies somewhat the proof of Lemma 6.1. 20 pages