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

  • Andriy I. BanduraEmail author
  • Oleh B. Skaskiv
Article
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Abstract

We obtain the sufficient conditions of boundedness of L-index in joint variables for analytic functions in the unit ball, where \( L:{\mathbb{C}}^n\to {\mathbb{R}}_{+}^n \) is a continuous positive vector-function. They give an stimate 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.

Keywords

Analytic function unit ball bounded L-index in joint variables maximum modulus partial derivative, minimum modulus, distribution of zeros, skeleton of polydisc. 

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Authors and Affiliations

  1. 1.Ivano-Frankivsk National Technical University of Oil and GasIvano-FrankivskUkraine
  2. 2.Ivan Franko National University of LvivLvivUkraine

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