Some improvements of criteria of L-index boundedness in direction

Author
A. I. Bandura
Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine
Abstract
In this paper, we improve criteria of boundedness of $L$-index in direction for entire functions in $\mathbb{C}^n.$ They give an estimate of maximum modulus on circles of various radius, maximum modulus by minimum modulus on circle and describe the behavior of directional logarithmic derivative and the distribution of zeros. The obtained results are also new for entire functions of bounded index in $\mathbb{C}.$
Keywords
entire function; bounded L-index in direction; distribution of zeros; directional logarithmic derivative
DOI
doi:10.15330/ms.47.1.27-32
Reference
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Pages
27-32
Volume
47
Issue
1
Year
2017
Journal
Matematychni Studii
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