Multisummability in Carleman ultraholomorphic classes by means of nonzero proximate orders
We introduce a general multisummability theory of formal power series in Carleman ultraholomorphic classes. The finitely many levels of summation are determined by pairwise comparable, nonequivalent weight sequences admitting nonzero proximate orders and whose growth indices are distinct. Thus, we e...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Universidad de Alcalá (UAH) |
| Repository: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Language: | English |
| OAI Identifier: | oai:ebuah.uah.es:10017/63861 |
| Online Access: | http://hdl.handle.net/10017/63861 https://dx.doi.org/10.1016/j.jmaa.2018.11.043 |
| Access Level: | Open access |
| Keyword: | Summability of formal power series Asymptotic expansions Carleman ultraholomorphic classes Proximate order Regular variation Laplace transform Matemáticas Mathematics |
| Summary: | We introduce a general multisummability theory of formal power series in Carleman ultraholomorphic classes. The finitely many levels of summation are determined by pairwise comparable, nonequivalent weight sequences admitting nonzero proximate orders and whose growth indices are distinct. Thus, we extend the powerful multisummability theory for finitely many Gevrey levels, developed by J.-P. Ramis, J. Écalle and W. Balser, among others. We provide both the analytical and cohomological approaches, and obtain a reconstruction formula for the multisum of a multisummable series by means of iterated generalized Laplace-like operators. |
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