Geodesic
Asymptotic estimates of entire functions of bounded $\mathbf{L}$-index in joint variables
Novi Sad Journal of Mathematics, Tome 48 (2018) no. 1.

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In this paper growth estimates of entire in $\mathbb{C}^n$ function of bounded $\mathbf{L}$-index in joint variables are obtained. They describe the behavior of maximum modulus of an entire function on a skeleton in a polydisc by behavior of the function $\mathbf{L}(z)=(l_1(z),\ldots,l_n(z)),$ where for every $j\in\{1,\ldots, n\}$ \ $l_j:\mathbb{C}^n\to \mathbb{R}_+$ is a continuous function. We generalized known results of W. K. Hayman, M. M. Sheremeta, A. D. Kuzyk and M. T. Borduyak to a wider class of functions $\mathbf{L}.$ One of our estimates is sharper even for entire in $\mathbb{C}$ functions of bounded $l$-index than Sheremeta's estimate.
Publié le :
DOI : 10.30755/NSJOM.06997
Classification : 32A15, 32A22, 32A40
Keywords: entire function, bounded $\mathbf{L}$-index in joint variables, maximum modulus, skeleton of polydisc, growth estimate, partial derivative 
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     author = {Andriy Bandura and Oleh Skaskiv},
     title = {Asymptotic estimates of entire functions of bounded $\mathbf{L}$-index in joint variables},
     journal = {Novi Sad Journal of Mathematics},
     pages = {103 - 116},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2018},
     doi = {10.30755/NSJOM.06997},
     url = {http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.06997/}
}
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Andriy Bandura; Oleh Skaskiv. Asymptotic estimates of entire functions of bounded $\mathbf{L}$-index in joint variables. Novi Sad Journal of Mathematics, Tome 48 (2018) no. 1. doi : 10.30755/NSJOM.06997. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.06997/

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