Entire functions of exponential type not vanishing in the half-plane Iz>k, where k>0
Journal Title: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica - Year 2017, Vol 71, Issue 1
Abstract
Let P(z) be a polynomial of degree n having no zeros in |z|<k, k≤1, and let Q(z):=znP(1/z). It was shown by Govil that if max|z|=1|P′(z)| and max|z|=1|Q′(z)| are attained at the same point of the unit circle |z|=1, then max|z|=1|P′(z)|≤n/(1+kn)max|z|=1|P(z)|. The main result of the present article is a generalization of Govil's polynomial inequality to a class of entire functions of exponential type.
Authors and Affiliations
Mohamed Hachani
Keywords
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- EP ID EP304586
- DOI 10.17951/a.2017.71.1.31
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