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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
Publisher: Springer Nature
Year of publication: 2020
No. of pages: 26
Publication type: Article
DOI: 10.1007/s12220-019-00203-5
ISSN: 1050-6926,1559-002X
Spanish project: MTM2016-77642-C2-1-P
Publication Url: https://doi.org/10.1007/s12220-019-00203-5
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JESUS JAVIER JIMENEZ GARRIDO
SANZ, JAVIER
SCHINDL, GERHARD
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