Optimal Flat Functions in Carleman–Roumieu Ultraholomorphic Classes in Sectors

We construct optimal flat functions in Carleman–Roumieu ultraholomorphic classes associated to general strongly nonquasianalytic weight sequences, and defined on sectors of suitably restricted opening. A general procedure is presented in order to obtain linear continuous extension operators, right i...

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Autores principales: Jiménez-Garrido, Javier, Miguel-Cantero, Ignacio, Sanz, Javier, Schindl, Gerhard
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10011312/
https://www.ncbi.nlm.nih.gov/pubmed/36938127
http://dx.doi.org/10.1007/s00025-023-01859-w
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author Jiménez-Garrido, Javier
Miguel-Cantero, Ignacio
Sanz, Javier
Schindl, Gerhard
author_facet Jiménez-Garrido, Javier
Miguel-Cantero, Ignacio
Sanz, Javier
Schindl, Gerhard
author_sort Jiménez-Garrido, Javier
collection PubMed
description We construct optimal flat functions in Carleman–Roumieu ultraholomorphic classes associated to general strongly nonquasianalytic weight sequences, and defined on sectors of suitably restricted opening. A general procedure is presented in order to obtain linear continuous extension operators, right inverses of the Borel map, for the case of regular weight sequences in the sense of Dyn’kin. Finally, we discuss some examples (including the well-known q-Gevrey case) where such optimal flat functions can be obtained in a more explicit way.
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spelling pubmed-100113122023-03-15 Optimal Flat Functions in Carleman–Roumieu Ultraholomorphic Classes in Sectors Jiménez-Garrido, Javier Miguel-Cantero, Ignacio Sanz, Javier Schindl, Gerhard Results Math Article We construct optimal flat functions in Carleman–Roumieu ultraholomorphic classes associated to general strongly nonquasianalytic weight sequences, and defined on sectors of suitably restricted opening. A general procedure is presented in order to obtain linear continuous extension operators, right inverses of the Borel map, for the case of regular weight sequences in the sense of Dyn’kin. Finally, we discuss some examples (including the well-known q-Gevrey case) where such optimal flat functions can be obtained in a more explicit way. Springer International Publishing 2023-03-14 2023 /pmc/articles/PMC10011312/ /pubmed/36938127 http://dx.doi.org/10.1007/s00025-023-01859-w Text en © The Author(s) 2023 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
Miguel-Cantero, Ignacio
Sanz, Javier
Schindl, Gerhard
Optimal Flat Functions in Carleman–Roumieu Ultraholomorphic Classes in Sectors
title Optimal Flat Functions in Carleman–Roumieu Ultraholomorphic Classes in Sectors
title_full Optimal Flat Functions in Carleman–Roumieu Ultraholomorphic Classes in Sectors
title_fullStr Optimal Flat Functions in Carleman–Roumieu Ultraholomorphic Classes in Sectors
title_full_unstemmed Optimal Flat Functions in Carleman–Roumieu Ultraholomorphic Classes in Sectors
title_short Optimal Flat Functions in Carleman–Roumieu Ultraholomorphic Classes in Sectors
title_sort optimal flat functions in carleman–roumieu ultraholomorphic classes in sectors
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10011312/
https://www.ncbi.nlm.nih.gov/pubmed/36938127
http://dx.doi.org/10.1007/s00025-023-01859-w
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