# Composition of entire functions and bounded L-index in direction

Author
Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine
Abstract
In the present paper we give an answer to the following question: Let $f\colon \mathbb{C}\to \mathbb{C}$ be an entire function of bounded $l$-index, $\Phi\colon \mathbb{C}^n\to \mathbb{C}$ be an entire function, $n\geq2,$ $l\colon \mathbb{C}\to \mathbb{R}_+$ be a continuous function. What are a positive continuous function $L\colon \mathbb{C}^n\to \mathbb{R}_+$ and a direction $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$ such that the composite function $f(\Phi(z))$ has bounded $L$-index in the direction $\mathbf{b}$?
Keywords
entire function; bounded L-index in direction; composite function; bounded l-index
DOI
doi:10.15330/ms.47.2.179-184
Reference
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Pages
179-184
Volume
47
Issue
2
Year
2017
Journal
Matematychni Studii
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