Extension operators for some ultraholomorphic classes defined by sequences of rapid growth
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 op...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/60200 |
| Acceso en línea: | http://hdl.handle.net/10017/60200 https://dx.doi.org/10.1007/s00365-023-09663-z |
| Access Level: | acceso abierto |
| Palabra clave: | Linear extension operators Asymptotic expansions Carleman ultraholomorphic classes Lambert function Laplace transform Matemáticas Mathematics |
| Sumario: | 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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