Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting

We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give ve...

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Detalles Bibliográficos
Autores principales: Boiti, Chiara, Jornet, David, Oliaro, Alessandro, Schindl, Gerhard
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2020
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7594626/
https://www.ncbi.nlm.nih.gov/pubmed/33184613
http://dx.doi.org/10.1007/s43037-020-00090-x
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author Boiti, Chiara
Jornet, David
Oliaro, Alessandro
Schindl, Gerhard
author_facet Boiti, Chiara
Jornet, David
Oliaro, Alessandro
Schindl, Gerhard
author_sort Boiti, Chiara
collection PubMed
description We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results for spaces defined by weight functions.
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spelling pubmed-75946262020-11-10 Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting Boiti, Chiara Jornet, David Oliaro, Alessandro Schindl, Gerhard Banach J Math Anal Original Paper We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results for spaces defined by weight functions. Springer International Publishing 2020-10-19 2021 /pmc/articles/PMC7594626/ /pubmed/33184613 http://dx.doi.org/10.1007/s43037-020-00090-x Text en © The Author(s) 2020 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/.
spellingShingle Original Paper
Boiti, Chiara
Jornet, David
Oliaro, Alessandro
Schindl, Gerhard
Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
title Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
title_full Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
title_fullStr Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
title_full_unstemmed Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
title_short Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
title_sort nuclear global spaces of ultradifferentiable functions in the matrix weighted setting
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7594626/
https://www.ncbi.nlm.nih.gov/pubmed/33184613
http://dx.doi.org/10.1007/s43037-020-00090-x
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