Nonlinear Conditions for Ultradifferentiability

A remarkable theorem of Joris states that a function f is [Formula: see text] if two relatively prime powers of f are [Formula: see text] . 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 r...

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Autores principales: Nenning, David Nicolas, Rainer, Armin, Schindl, Gerhard
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550781/
https://www.ncbi.nlm.nih.gov/pubmed/34720560
http://dx.doi.org/10.1007/s12220-021-00718-w
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author Nenning, David Nicolas
Rainer, Armin
Schindl, Gerhard
author_facet Nenning, David Nicolas
Rainer, Armin
Schindl, Gerhard
author_sort Nenning, David Nicolas
collection PubMed
description A remarkable theorem of Joris states that a function f is [Formula: see text] if two relatively prime powers of f are [Formula: see text] . 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.
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spelling pubmed-85507812021-10-29 Nonlinear Conditions for Ultradifferentiability Nenning, David Nicolas Rainer, Armin Schindl, Gerhard J Geom Anal Article A remarkable theorem of Joris states that a function f is [Formula: see text] if two relatively prime powers of f are [Formula: see text] . 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. Springer US 2021-06-19 2021 /pmc/articles/PMC8550781/ /pubmed/34720560 http://dx.doi.org/10.1007/s12220-021-00718-w Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Nenning, David Nicolas
Rainer, Armin
Schindl, Gerhard
Nonlinear Conditions for Ultradifferentiability
title Nonlinear Conditions for Ultradifferentiability
title_full Nonlinear Conditions for Ultradifferentiability
title_fullStr Nonlinear Conditions for Ultradifferentiability
title_full_unstemmed Nonlinear Conditions for Ultradifferentiability
title_short Nonlinear Conditions for Ultradifferentiability
title_sort nonlinear conditions for ultradifferentiability
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550781/
https://www.ncbi.nlm.nih.gov/pubmed/34720560
http://dx.doi.org/10.1007/s12220-021-00718-w
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