Geodesic
Boundedness of $\mathbf L$-Index in Joint Variables for Sum of Entire Functions
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 4, p. 595

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In the paper, we present sufficient conditions of boundedness of $\mathbf{L}$-index in joint variables for a sum of entire functions, where $\mathbf{L}:\mathbb{C}^n\to\mathbb{R}^n_+$ is a continuous function, $\mathbb{R}_+=(0,+\infty)$. They are applicable to a very wide class of entire functions because for every entire function $F$ in $\mathbb{C}^n$ with bounded multiplicities of zero points there exists a positive continuous function $\mathbf{L}$ such that $F$ has bounded $\mathbf{L}$-index in joint variables. Our propositions are generalizations of Pugh's result obtained for entire functions of one variable of bounded index.
Classification : 32A15 32A17, 30D20
Keywords: Entire function of several variables, bounded $\mathbfL$-index in joint variables, sum of entire functions 
A. Bandura. Boundedness of $\mathbf L$-Index in Joint Variables for Sum of Entire Functions. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 4, p. 595 . http://geodesic.mathdoc.fr/item/KJM_2022_46_4_a5/
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     title = {Boundedness of $\mathbf L${-Index} in {Joint} {Variables} for {Sum} of {Entire} {Functions}},
     journal = {Kragujevac Journal of Mathematics},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/KJM_2022_46_4_a5/}
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