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2019 Functions analytic in the unit ball having bounded $L$-index in a direction
Andriy Bandura, Oleh Skaskiv
Rocky Mountain J. Math. 49(4): 1063-1092 (2019). DOI: 10.1216/RMJ-2019-49-4-1063

Abstract

We propose a generalization of a concept of bounded index for analytic functions in the unit ball. Use of directional derivatives gives us a possibility to deduce the necessary and sufficient conditions of boundedness of $L$-index in a direction for analytic functions of several variables, namely, we obtain an analog of Hayman's theorem and a logarithmic criteria for this class. The criteria describe the behavior of the directional logarithmic derivative outside the zero set and a uniform distribution of zeros in some sense. The criteria are useful for studying analytic solutions of partial differential equations and estimating their growth. We present a scheme of this application.

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Andriy Bandura. Oleh Skaskiv. "Functions analytic in the unit ball having bounded $L$-index in a direction." Rocky Mountain J. Math. 49 (4) 1063 - 1092, 2019. https://doi.org/10.1216/RMJ-2019-49-4-1063

Information

Published: 2019
First available in Project Euclid: 29 August 2019

zbMATH: 07104706
MathSciNet: MR3998910
Digital Object Identifier: 10.1216/RMJ-2019-49-4-1063

Subjects:
Primary: 32A10‎
Secondary: 32A17, 35B08

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 4 • 2019
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