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 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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     author = {A. Bandura},
     title = {Boundedness of $\mathbf L${-Index} in {Joint} {Variables} for {Sum} of {Entire} {Functions}},
     journal = {Kragujevac Journal of Mathematics},
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     number = {4},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2022_46_4_a5/}
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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/