Log-convex sequences and nonzero proximate orders

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:448

Article

Jimenez-Garrido, Javier¹  Sanz, Javier¹  Schindl, Gerhard² 

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

[2] Univ Vienna, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

关键词: Log-convex sequences;    Regular variation;    Proximate orders;    Carleman ultraholomorphic classes;   

DOI  :  10.1016/j.jmaa.2016.11.069

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 [10], and their validity depends on the possibility of associating to M 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free