Partial logarithmic derivatives and distribution of zeros of analytic functions in the unit ball of bounded L-index in joint variables

We obtain the sufficient conditions of boundedness of L-index in joint variables for analytic functions in the unit ball, where L : Cⁿ → Rⁿ₊ is a continuous positive vector-function. They give an estimate of the maximum modulus of an analytic function by its minimum modulus on a skeleton in a polydi...

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Published in:Український математичний вісник
Date:2018
Main Authors: Bandura, A.I., Skaskiv, O.B.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/169396
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Partial logarithmic derivatives and distribution of zeros of analytic functions in the unit ball of bounded L-index in joint variables / A.I. Bandura, O.B. Skaskiv // Український математичний вісник. — 2018. — Т. 15, № 2. — С. 177-193. — Бібліогр.: 37 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:We obtain the sufficient conditions of boundedness of L-index in joint variables for analytic functions in the unit ball, where L : Cⁿ → Rⁿ₊ is a continuous positive vector-function. They give an estimate of the maximum modulus of an analytic function by its minimum modulus on a skeleton in a polydisc and describe the behavior of all partial logarithmic derivatives outside some exceptional set and the distribution of zeros. The deduced results are also new for analytic functions in the unit disc of bounded index and l-index. They generalize known results by G. H. Fricke, M. M. Sheremeta, A. D. Kuzyk, and V. O. Kushnir.
ISSN:1810-3200