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Multisummability in Carleman ultraholomorphic classes by means of nonzero proximate orders

Abstract: 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.

 Fuente: Journal of Mathematical Analysis and Applications, Volume 472, Issue 1, 1 April 2019, Pages 627-686

 Editorial: Academic Press Inc.

 Fecha de publicación: 01/04/2019

 Nº de páginas: 60

 Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jmaa.2018.11.043

 ISSN: 0022-247X,1096-0813

 Proyecto español: MTM2016-77642-C2-1-P

 Url de la publicación: https://doi.org/10.1016/j.jmaa.2018.11.043

Autoría

JESUS JAVIER JIMENEZ GARRIDO

KAMIMOTO, SHINGO

LASTRA, ALBERTO

SANZ, JAVIER