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Injectivity and surjectivity of the asymptotic Borel map in Carleman ultraholomorphic classes

Abstract: We consider Roumieu?Carleman ultraholomorphic classes and classes of functions admitting asymptotic expansion in unbounded sectors, defined in terms of a log-convex sequence . Departing from previous results by S. Mandelbrojt and B. Rodríguez-Salinas, we completely characterize the injectivity of the Borel map by means of the theory of proximate orders: A growth index turns out to put apart the values of the opening of the sector for which injectivity holds or not. In the case of surjectivity, we considerably extend partial results by J. Schmets and M. Valdivia and by V. Thilliez, and prove a similar dividing character for the index (introduced by Thilliez, and generally different from ) in some standard situations (for example, as far as is strongly regular).

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Journal of Mathematical Analysis and Applications, Volume 469, Issue 1, 1 January 2019, Pages 136-168

Editorial: Academic Press Inc.

 Fecha de publicación: 01/01/2019

Nº de páginas: 33

Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jmaa.2018.09.011

ISSN: 0022-247X,1096-0813

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

Url de la publicación: https://doi.org/10.1016/j.jmaa.2018.09.011