A Phragmen-Lindelof Theorem via Proximate Orders, and the Propagation of Asymptotics

Autor(en)

Javier Jiménez-Garrido, Javier Sanz, Gerhard Schindl

Abstrakt

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 Phragmen-Lindelof theorem, here obtained for functions whose growth in a sector is specified by a nonzero proximate order in the sense of Lindelof and Valiron.

Organisation(en)

Institut für Mathematik

Externe Organisation(en)

University of Valladolid

Journal

Journal of Geometric Analysis

Band

30

Seiten

3458-3483

ISSN

1050-6926

DOI

https://doi.org/10.1007/s12220-019-00203-5

Publikationsdatum

2019

Peer-reviewed

Ja

ÖFOS 2012

101002 Analysis

Schlagwörter

ASJC Scopus Sachgebiete

Geometry and Topology

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/2b712e3f-a743-4288-a374-c54099cdc709