Summability in general Carleman ultraholomorphic classes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:430

Article

Lastra, Alberto¹  Malek, Stephane²  Sanz, Javier³ 

[1] Univ Alcala de Henares, Dept Fis & Matemat, Madrid 28871, Spain

[2] UFR Math Pures & Appl, F-59655 Villeneuve Dascq, France

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

关键词: Laplace and Borel transforms;    Formal power series;    Asymptotic expansions;    Ultraholomorphic classes;    Summability;    Moment-partial differential equations;   

DOI  :  10.1016/j.jmaa.2015.05.046

来源: Elsevier

【 摘 要 】

A definition of summability is put forward in the framework of general Carleman ultraholomorphic classes in sectors, so generalizing k-summability theory as developed by J.-P. Ramis. Departing from a strongly regular sequence of positive numbers, we construct an associated analytic proximate order and corresponding kernels, which allow us to consider suitable Laplace and Borel-type transforms, both formal and analytic, whose behavior closely resembles that of the classical ones in the Gevrey case. An application to the study of the summability properties of the formal solutions to some moment-partial differential equations is included. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free