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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

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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.

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Authors and Affiliations

  1. Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine

    Andriy I. Bandura

  2. Ivan Franko National University of Lviv, Lviv, Ukraine

    Oleh B. Skaskiv

Authors
  1. Andriy I. Bandura
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  2. Oleh B. Skaskiv
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Correspondence to Andriy I. Bandura.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 15, No. 2, pp. 177–193, January–March, 2018.

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Bandura, A.I., Skaskiv, O.B. Partial logarithmic derivatives and distribution of zeros of analytic functions in the unit ball of bounded L-index in joint variables. J Math Sci 239, 17–29 (2019). https://doi.org/10.1007/s10958-019-04284-z

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