Continuous right inverses for the asymptotic Borel map in ultraholomorphic classes via a Laplace-type transform

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:396

Article

Lastra, Alberto¹  Malek, Stephane²  Sanz, Javier³ 

[1] Univ Alcala, Dept Matemat, Madrid 28871, Spain

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

[3] Univ Valladolid, Fac Ciencias, Inst Invest Matemat, Dept Anal Matemat,IMUVA, E-47005 Valladolid, Spain

关键词: Laplace transform;    Formal power series;    Asymptotic expansions;    Ultraholomorphic classes;    Borel map;    Extension operators;   

DOI  :  10.1016/j.jmaa.2012.07.013

来源: Elsevier

【 摘 要 】

A new construction of linear continuous right inverses for the asymptotic Borel map is provided in the framework of general Carleman ultraholomorphic classes in narrow sectors. Such operators were already obtained by V. Thilliez by means of Whitney extension results for non quasianalytic ultradifferentiable classes, due to J. Chaumat and A.M. Chollet, but our approach is completely different, resting on the introduction of a suitable truncated Laplace-type transform. This technique is better suited for a generalization of these results to the several variables setting. Moreover, it closely resembles the classical procedure in the case of Gevrey classes, so indicating the way for the introduction of a concept of summability which generalizes k-summability theory as developed by J.P. Ramis. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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