Strong asymptotic expansions in a multidirection

Details Strong asymptotic expansions in a multidirection Strong asymptotic expansions in a multidirection

2011-03-23

arxiv.org/abs/1103.4600v1

Mathematics

Complex Variables

25 pages

Scientific paper

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.

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