Entire functions of exponential type not vanishing in the half-plane Iz>k, where k>0

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

Related Articles

The constructions of general connections on the fibred product of q copies of the first jet prolongation

We describe all natural operators A transforming general connections Gamma on fibred manifolds Y -> M and torsion-free classical linear connections Gamma on M into general connections A(Gamma, Lambda) on the fibred produ...

The generalized Day norm. Part I. Properties

In this paper we introduce a modification of the Day norm in c0(Γ) and investigate properties of this norm.

Invo-regular unital rings

It was asked by Nicholson (Comm. Algebra, 1999) whether or not unit-regular rings are themselves strongly clean. Although they are clean as proved by Camillo–Khurana (Comm. Algebra, 2001), recently Nielsen and ˇSter show...

Periodic solutions of Euler-Lagrange equations with sublinear potentials in an Orlicz-Sobolev space setting

In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space W1LΦ([0,T]). We employ the direct method of calculus of variations and we consider a potential functio...

On almost complex structures from classical linear connections

Let Mfm be the category of m-dimensional manifolds and local diffeomorphisms and let T be the tangent functor on Mfm. Let V be the category of real vector spaces and linear maps and let Vm be the category of m-dimension...

Download PDF file
  • EP ID EP304586
  • DOI 10.17951/a.2017.71.1.31
  • Views 108
  • Downloads 0

How To Cite

Mohamed Hachani (2017). Entire functions of exponential type not vanishing in the half-plane Iz>k, where k>0. Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica, 71(1), 31-39. https://europub.co.uk/articles/-A-304586