Strongly regular sequences and proximate orders

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:438

Article

Jimenez-Garrido, Javier¹  Sanz, Javier¹ 

[1] Univ Valladolid, Fac Ciencias, Dept Algebra Anal Matemat Geometria & Topol, Inst Invest Matemat,IMUVA, E-47011 Valladolid, Spain

关键词: Strongly regular sequences;    Regular variation;    Proximate orders;    Ultraholomorphic classes;    Watson's Lemma;   

DOI  :  10.1016/j.jmaa.2016.02.010

来源: Elsevier

【 摘 要 】

Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence M = (M-p)(p is an element of N0), have been put forward by A. Lastra, S. Malek and the second author [28]. We study several open questions related to the existence of kernels of summability constructed by means of analytic proximate orders. In particular, we give a simple condition that allows us to associate a proximate order with a strongly regular sequence. Under this assumption, and through the characterization of strongly regular sequences in terms of so-called regular variation, we show that the growth index-gamma(M) defined by V. Thilliez [54] and the order of quasianalyticity omega(M) introduced by the second author [50] are the same. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free