Small entire functions with extremely fast growth
type: Item
instance of: scholarly article
title: Small entire functions with extremely fast growth
zbMATH Open document ID: 0872.30022
author: L. Bernal-González
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-10-15T00:00:00Z
review text: Generalizing his earlier results [ibid. 201, No. 3, 1002-1009 (1996; Zbl 0855.30030)] the author produces a linear space \(M\) of entire functions dense in the space of all entire functions such that for every \(f\in M\), \(\exp(|z|^\alpha)f^{(j)} (z)\to 0\) for \(z\to\infty\) in \(S\) and all \(j\in\mathbb{N}_0\), \(\int_\ell f^{(j)}ds=0\) for all \(j\in\mathbb{N}_0\) and all straight lines \(\ell\), while \(f\) is `very large' (infinite growth index) globally. Here \(S\) is any sector with tip at 0, or any parallel strip, and \(\alpha\) is any number in \((0,\frac{1}{2})\). The main tool is a theorem by Arakelian on approximation with speed of a function \(g\in A(F)\) by entire functions, if \(F\) is an Arakelian set.
Mathematics Subject Classification ID: 30E15
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 1005695
zbMATH Keywords: entire functions
reviewed by: Dieter Gaier
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5312
OpenAlex ID: W1968540744
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DOI: 10.1006/JMAA.1997.5312
description: scientific article; zbMATH DE number 1005695