Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation

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) wei...

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Autores principales: Jiménez-Garrido, Javier, Sanz, Javier, Schindl, Gerhard
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8643302/
https://www.ncbi.nlm.nih.gov/pubmed/34924811
http://dx.doi.org/10.1007/s00025-021-01566-4
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author Jiménez-Garrido, Javier
Sanz, Javier
Schindl, Gerhard
author_facet Jiménez-Garrido, Javier
Sanz, Javier
Schindl, Gerhard
author_sort Jiménez-Garrido, Javier
collection PubMed
description 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.
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spelling pubmed-86433022021-12-15 Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation Jiménez-Garrido, Javier Sanz, Javier Schindl, Gerhard Results Math Article 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. Springer International Publishing 2021-12-04 2022 /pmc/articles/PMC8643302/ /pubmed/34924811 http://dx.doi.org/10.1007/s00025-021-01566-4 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
Jiménez-Garrido, Javier
Sanz, Javier
Schindl, Gerhard
Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation
title Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation
title_full Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation
title_fullStr Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation
title_full_unstemmed Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation
title_short Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation
title_sort equality of ultradifferentiable classes by means of indices of mixed o-regular variation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8643302/
https://www.ncbi.nlm.nih.gov/pubmed/34924811
http://dx.doi.org/10.1007/s00025-021-01566-4
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