A Phragmén-Lindelöf Theorem via Proximate Orders, and the Propagation of Asymptotics.

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-01-01 Epub Date: 2019-05-10 DOI:10.1007/s12220-019-00203-5

Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl

引用次数: 1

Abstract

We prove that, for asymptotically bounded holomorphic functions in a sector in $C,$ an asymptotic expansion in a single direction towards the vertex with constraints in terms of a logarithmically convex sequence admitting a nonzero proximate order entails asymptotic expansion in the whole sector with control in terms of the same sequence. This generalizes a result by Fruchard and Zhang for Gevrey asymptotic expansions, and the proof strongly rests on a suitably refined version of the classical Phragmén-Lindelöf theorem, here obtained for functions whose growth in a sector is specified by a nonzero proximate order in the sense of Lindelöf and Valiron.

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一个近似阶的Phragmén-Lindelöf定理，以及渐近的传播。

证明了C中扇形上的渐近有界全纯函数，在约束为非零近似阶的对数凸序列的条件下，向顶点的单向渐近展开式需要在控制为同一序列的整个扇形上的渐近展开式。这推广了Fruchard和Zhang关于Gevrey渐近展开的结果，并且该证明强烈地依赖于经典Phragmén-Lindelöf定理的一个适当的改进版本，这里得到的函数在一个扇形中的增长是由Lindelöf和Valiron意义上的非零近似阶指定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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