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Log-convex sequences and nonzero proximate orders

Abstract: Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence , have been put forward by A. Lastra, S. Malek and the second author, and their validity depends on the possibility of associating to a nonzero proximate order. We provide several characterizations of this and other related properties, in which the concept of regular variation for functions and sequences plays a prominent role. In particular, we show how to construct well-behaved strongly regular sequences from nonzero proximate orders.

 Fuente: Journal of Mathematical Analysis and Applications, Volume 448, Issue 2, 15 April 2017, Pages 1572-1599

 Editorial: Academic Press Inc.

 Fecha de publicación: 15/04/2017

 Nº de páginas: 28

 Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jmaa.2016.11.069

 ISSN: 0022-247X,1096-0813

 Proyecto español: MTM2012-31439.

 Url de la publicación: https://doi.org/10.1016/j.jmaa.2016.11.069