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

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.

 Fuente: The Journal of Geometric Analysis 2020, 30, 3458-3483

Editorial: Springer Nature

 Año de publicación: 2020

Nº de páginas: 26

Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s12220-019-00203-5

ISSN: 1050-6926,1559-002X

Proyecto español: MTM2016-77642-C2-1-P

Url de la publicación: https://doi.org/10.1007/s12220-019-00203-5

Autores/as

SCHINDL, GERHARD