Extension operators for some ultraholomorphic classes defined by sequences of rapid growth
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/60200DOI: 10.1007/s00365-023-09663-z
ISSN: 0176-4276
Publisher
Springer
Date
2023-07-15Embargo end date
2024-07-15Funders
Agencia Estatal de Investigación
Universidad de Alcalá
Bibliographic citation
Jiménez Garrido, J., Lastra Sedano, A. & Sanz, J. 2023, “Extension operators for some ultraholomorphic classes defined by sequences of rapid growth”, Constructive Approximation, pp. 1-23.
Keywords
Linear extension operators
Asymptotic expansions
Carleman ultraholomorphic classes
Lambert function
Laplace transform
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105621GB-I00/ES/METODOS ASINTOTICOS, ALGEBRAICOS Y GEOMETRICOS EN FOLIACIONES SINGULARES Y SISTEMAS DINAMICOS/
info:eu-repo/grantAgreement/UAH//CM-JIN-2021-014
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica, Técnica y de Innovación 2021-2023/TED2021-129813A-I00
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1007/s00365-023-09663-zRights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2023 The Authors, under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature
Access rights
info:eu-repo/semantics/embargoedAccess
Abstract
While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid growth, there is no general procedure to construct extension operators in this case. We do provide such operators in complex sectors for some particular classes considered by S. Pilipović, N. Teofanov and F. Tomić in the ultradifferentiable setting. Although these classes are, in their words, “beyond Gevrey regularity”, in some cases they keep the property of stability under differentiation, which is crucial for our technique, based on formal Borel- and truncated Laplace-like transforms with suitable kernels.
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