Continuous right inverses for the asymptotic Borel map in ultraholomorphic classes via a Laplace-type transform
Identificadores
Enlace permanente (URI): http://hdl.handle.net/10017/41449DOI: 10.1016/j.jmaa.2012.07.013
ISSN: 0022-247X
Editor
Elsevier
Fecha de publicación
2012-12-15Patrocinadores
Ministerio de Ciencia e Innovación
Cita bibliográfica
Lastra, A., Malek, S. & Sanz, J. 2012, “Continuous right inverses for the asymptotic Borel map in ultraholomorphic classes via a Laplace-type transform”, Journal of Mathematical Analysis and Applications, vol. 396, no. 2, pp. 724-740
Palabras clave
Laplace transform
Formal power series
Asymptotic expansions
Ultraholomorphic classes
Borel map
Extension operators
Proyectos
info:eu-repo/grantAgreement/MICINN//MTM2009-12561/ES/Estudio De La Dependencia Respecto De Los Parametros De Las Soluciones De Ciertas Ecuaciones De La Fisica Matematica/
Tipo de documento
info:eu-repo/semantics/article
Versión
info:eu-repo/semantics/acceptedVersion
Versión del editor
https://doi.org/10.1016/j.jmaa.2012.07.013Derechos
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2012 Elsevier
Derechos de acceso
info:eu-repo/semantics/openAccess
Resumen
A new construction of linear continuous right inverses for the asymptotic Borel map is provided in the framework of general Carleman ultraholomorphic classes in narrow sectors. Such operators were already obtained by V. Thilliez by means of Whitney extension results for non quasianalytic ultradifferentiable classes, due to J. Chaumat and A. M. Chollet, but our approach is completely different, resting on the introduction of a suitable truncated Laplace-type transform. This technique is better suited for a generalization of these results to the several variables setting. Moreover, it closely resembles the classical procedure in the case of Gevrey classes, so indicating the way for the introduction of a concept of summability which generalizes k-summability theory as developed by J. P. Ramis.
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Colecciones
- MATEMATIC - Artículos [172]