Sufficient conditions of boundedness of Lindex in joint variables 

Author 
andriykopanytsia@gmail.com; mbordulyak@yahoo.com, olskask@gmail.com
Department of Higher Mathematics
IvanoFrankivs’k National Technical University of Oil and Gas; Department of Function Theory and Theory of Probability
Ivan Franko National University of Lviv

Abstract 
A concept of boundedness of $\mathbf{L}$index in joint variables (see in Bordulyak M.T. The space of entire in $\mathbb{C}^n$ functions of bounded $L$index, Mat. Stud., 4 (1995), 5358. (in Ukrainian)) is generalised for $\mathbf{L}(z)=(l_1(z),$ $\ldots,$ $l_{n}(z)),$
$z\in\mathbb{C}^n.$ We proved criteria of boundedness of $\mathbf{L}$index in joint variables
and established a connection between the classes of entire functions of bounded $l_j$index in each direction $\mathbf{e}_j$ and functions of bounded $\mathbf{L}$index in joint variables.
We deduce new sufficient conditions of boundedness of $\mathbf{L}$index in joint variables. The obtained restrictions describe the behaviour of logarithmic derivative in each variable and the distribution of zeros.

Keywords 
entire function; bounded Lindex in joint variables; bounded Lindex in direction; directional
logarithmic derivative; distibution of zeros

DOI 
doi:10.15330/ms.45.1.1226

Reference 
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Pages 
1226

Volume 
45

Issue 
1

Year 
2016

Journal 
Matematychni Studii

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