Injectivity and surjectivity of the asymptotic Borel map in Carleman ultraholomorphic classes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:469

Article

Jimenez-Garrido, Javier^1,2  Sanz, Javier^1,2  Schindl, Gerhard¹ 

[1] Univ Valladolid, Dept Algebra Anal Matemat Geometria & Topol, Fac Ciencias, Paseo de Belen 7, E-47011 Valladolid, Spain

[2] Inst Invest Matemat IMUVA, Valladolid, Spain

关键词: Carleman ultraholomorphic classes;    Asymptotic expansions;    Proximate order;    Borel-Ritt-Gevrey theorem;    Watson's lemma;    Laplace transform;   

DOI  :  10.1016/j.jmaa.2018.09.011

来源: Elsevier

【 摘 要 】

We consider Roumieu-Carleman ultraholomorphic classes and classes of functions admitting asymptotic expansion in unbounded sectors, defined in terms of a log-convex sequence M. Departing from previous results by S. Mandelbrojt and B. Rodriguez-Salinas, we completely characterize the injectivity of the Borel map by means of the theory of proximate orders: A growth index omega(M) turns out to put apart the values of the opening of the sector for which injectivity holds or not. In the case of surjectivity, we considerably extend partial results by J. Schmets and M. Valdivia and by V. Thilliez, and prove a similar dividing character for the index gamma(M) (introduced by Thilliez, and generally different from omega(M)) in some standard situations (for example, as far as M is strongly regular). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free