Entire functions of bounded L-index: its zeros and behavior of partial logarithmic derivatives
type: Item
instance of: scholarly article
title: Entire functions of bounded L-index: its zeros and behavior of partial logarithmic derivatives
zbMATH Open document ID: 1401.32004
DOI: 10.1155/2017/3253095
author: Andriy Bandura
author: O. B. Skaskīv
published in: Journal of Complex Analysis
publication date: 2018-10-01T00:00:00Z
review text: Summary: In this paper, we obtain new sufficient conditions of boundedness of \(\mathbf{L}\)-index in joint variables for entire function in \(\mathbb{C}^n\) functions. They give an estimate of maximum modulus of an entire function by its minimum modulus on a skeleton in a polydisc and describe the behavior of all partial logarithmic derivatives and the distribution of zeros. In some sense, the obtained results are new for entire functions of bounded index and \(l\)-index in \(\mathbb{C}\) too. They generalize known results of Fricke, Sheremeta, and Kuzyk.
Mathematics Subject Classification ID: 32A15
zbMATH DE Number: 6945693
zbMATH Keywords: entire functions of several variables
zbMATH Keywords: \(\mathbf L\)-index
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/3253095
OpenAlex ID: W2767733388
cites work: Sufficient conditions of boundedness of \(L\)-index in joint variables
cites work: Open problems for entire functions of bounded index in direction
cites work: Entire functions of several variables of bounded index
cites work: Q4788174
cites work: Q5604643
cites work: Entire bivariate functions of exponential type
cites work: Multivalence of bivariate functions of bounded index
cites work: A characterization of holomorphic bivariate functions of bounded index
cites work: A proof of Sheremeta's conjecture concerning an entire function of bounded \(l\)-index
cites work: Q4565543
cites work: Analytic functions of bounded index
cites work: Linear Differential Equations and Logarithmic Derivative Estimates
cites work: SHARP LOGARITHMIC DERIVATIVE ESTIMATES WITH APPLICATIONS TO ORDINARY DIFFERENTIAL EQUATIONS IN THE UNIT DISC
cites work: GENERALIZED LOGARITHMIC DERIVATIVE ESTIMATES OF GOL'DBERG–GRINSHTEIN TYPE
cites work: Growth estimates for logarithmic derivatives of Blaschke products and of functions in the Nevanlinna class
cites work: Local geometry of zero sets of holomorphic functions near the torus
cites work: Q4796442
cites work: Zero sets of functions in the Nevanlinna or the Nevanlinna-Djrbachian classes.
cites work: Remark on Zero Sets of Holomorphic Functions in Convex Domains of Finite Type
cites work: Gauss-Lucas theorems for entire functions onCM
cites work: An explicit calculation of the Ronkin function
cites work: Q3477141
cites work: Entire functions of locally slow growth
cites work: Logarithmic derivative and zeros of an entire function of bounded \(l\)- index
cites work: Q4774304
cites work: Functions of bounded index and their logarithmic derivatives
description: scientific article; zbMATH DE number 6945693