MR3012580 Alberto LASTRA, Jorge MOZO-FERNÁNDEZ and Javier SANZ Alberto LASTRA, Jorge MOZO-FERNÁNDEZ and Javier SANZ Strong Asymptotic Expansions in a Multidirection Funkcialaj Ekvacioj. Serio Internacia 55 2012 317--345 http://fe.math.kobe-u.ac.jp/FE/FullPapers/55-2/55_317.pdf http://www.ams.org/mathscinet-getitem?mr=MR3012580 In this paper we prove that, for asymptotically bounded holomorphic functions defined in a polysector in ${\mathbb C}^n$, the existence of a strong asymptotic expansion in Majima's sense following a single multidirection towards the vertex entails (global) asymptotic expansion in the whole polysector. Moreover, we specialize this result for Gevrey strong asymptotic expansions. This is a generalization of a result proved by A. Fruchard and C. Zhang for asymptotic expansions in one variable, but the proof, mainly in the Gevrey case, involves different techniques of a functional-analytic nature. Strong asymptotic expansions, Gevrey asymptotics, Laplace transform, Banach spaces analytic functions. 41A60, 41A63, 40C10, 46E15. 55-317 2012 Strong Asymptotic Expansions in a Multidirection Alberto LASTRA, Jorge MOZO-FERNÁNDEZ and Javier SANZ Alberto LASTRA, Jorge MOZO-FERNÁNDEZ and Javier SANZ 1 Balser, W. Formal power series and linear systems of meromorphic ordinary differential equations Universitext, Springer-Verlag, New York 2000 MR1722871
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