An inequality for entire functions of exponential type
type: Item
instance of: scholarly article
title: An inequality for entire functions of exponential type
zbMATH Open document ID: 0707.41022
DOI: 10.1016/0021-9045(89)90015-4
published in: Journal of Approximation Theory
publication date: 1989-01-01T00:00:00Z
review text: Using a result of \textit{L. Hörmander} [Math. Scand. 3, 21-27 (1955; Zbl 0065.303)] the author shows: Let f be entire, of exponential type \(\tau\), such that \(| f(x)| \leq 1\) for real x. If \(| f(0)| =\cos a\), \(0\leq a\leq \pi /2\) and \(f'(0)=0\), then \(| f(x)| \leq \sin [\{(\pi -a)^ 2+\tau^ 2x^ 2\}^{1/2}-\pi /2]\) for \(| x| <\{a(2\pi -a)\}^{1/2}/\tau\). Further \(| f''(0)| \leq (\sin a/a)\tau^ 2\).
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 4161365
author: Qazi M. Tariq
MaRDI profile type: Publication
full work available at URL: 0021-9045(89)90015-4
OpenAlex ID: W2067267489
cites work: Q3235904
cites work: Q5833361
cites work: Inequalities for Entire Functions of Exponential Type
cites work: Some inequalities for functions of exponential type
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description: scientific article; zbMATH DE number 4161365