Directional Logarithmic Derivative and the Distribution of Zeros of an Entire Function of Bounded L-Index Along the Direction

Bandura, Andriy; Скасків, О. Б.

doi:10.1007/s11253-017-1377-8

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Proof Of Main Theorem1

Of Bounded L-index In the Direction B If And Only If For Eve1

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Cited by 26 publications

(24 citation statements)

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“…The presented definition appeared for the first time in [6]. For n = 1 Theorem 2 is Sheremeta's result ( [16]).…”

Section: Proof Of Main Theoremmentioning

confidence: 99%

Composition of entire functions and bounded L-index in direction

Bandura

2016

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“…The presented definition appeared for the first time in [6]. For n = 1 Theorem 2 is Sheremeta's result ( [16]).…”

Section: Proof Of Main Theoremmentioning

confidence: 99%

Composition of entire functions and bounded L-index in direction

Bandura

2016

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“…Proof of Theorem 6 is similar to that the corresponding theorem from [1]. But our proof also uses Theorem 4 instead of Theorem 3 as in [1].…”

Section: Of Bounded L-index In the Direction B If And Only If For Evementioning

confidence: 90%

“…Introduction. This paper is an addendum to our paper [1]. We improve our solutions of some interesting problems in the theory of entire functions of bounded L-index in direction [2].…”

mentioning

confidence: 96%

“…We improve our solutions of some interesting problems in the theory of entire functions of bounded L-index in direction [2]. There were partially proved two conjectures about characterizations of functions from that class [1]. But we assumed that some inequalities are valid for a disk with radius in (0, 1).…”

mentioning

confidence: 99%

“…In particular, the following assertion is true. 1 and r 2 such that 0 < r 1 < r 2 < +∞ there exists a number…”

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confidence: 99%

See 2 more Smart Citations

Some improvements of criteria of $L$-index boundedness in direction

Bandura

2016

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Functions analytic in a unit ball of bounded L-index in joint variables

Bandura

Скасків

2017

J Math Sci

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A. I. Bandura, O. B. Skaskiv, Some properties of analytic in a ball functions of bounded L-index in joint variables A concept of boundedness of the L-index in joint variables (see in Bandura A. I., Bordulyak M. T., Skaskiv O. B. Sufficient conditions of boundedness of L-index in joint variables, Mat. Stud. 45 (2016), 12-26. dx.doi.org/10.15330/ms.45.1.12-26) is generalized for analytic in a ball function. There are proved criteria of boundedness of the L-index in joint variables which describe local behavior of partial derivatives and maximum modudus on a skeleton of a polydisc, properties of power series expansion. Also we obtained analog of Hayman's Theorem.As a result, they are applied to study linear higher-order systems of partial differential equations and to deduce sufficient conditions of boundedness of the L-index in joint variables for their analytic solutions and to estimate it growth.We used an exhaustion of ball in C n by polydiscs. Also growth estimates of analytic in ball functions of bounded L-index in joint variables are obtained. Note that this paper and paper "Analytic functions in a bidisc of bounded L-index in joint variables" (arXiv:1609.04190) do not overlap because analytic in a ball and analytic in a bidisc functions are different classes of holomorphic functions. Some results have similar formulations but a bidisc and a ball are particular geometric objects.

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Directional Logarithmic Derivative and the Distribution of Zeros of an Entire Function of Bounded L-Index Along the Direction

Cited by 26 publications

References 4 publications

Composition of entire functions and bounded L-index in direction

Composition of entire functions and bounded L-index in direction

Some improvements of criteria of $L$-index boundedness in direction

Functions analytic in a unit ball of bounded L-index in joint variables

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