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Proximate order and type of entire functions of several complex variables

Israel Journal of Mathematics, 1995
The \((p,q)\)-order, \((p,q)\)-type, and index-pair for entire functions of several complex variables are defined in this paper. Using these definitions, the authors generalize two growth theorems given by \textit{P. Lelong} and \textit{L. Gruman} in their book `Entire functions of several complex variables' (Chapter one), Springer-Verlag, Berlin (1986;
Einstein-Matthews, S. M., Kasana, H. S.
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Entire Functions of Several Complex Variables

, 1986
Pierre Lelong, Lawrence Gruman
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Growth of Entire Functions of Several Variables

, 1974
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Boundedness of L-Index for the Composition of Entire Functions of Several Variables

Ukrainian Mathematical Journal, 2019
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Bandura, A. I., Skaskiv, O. B.
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ON SUFFICIENT SETS IN SPACES OF ENTIRE FUNCTIONS OF SEVERAL VARIABLES

Mathematics of the USSR-Sbornik, 1989
Let D be a convex bounded domain in \({\mathbb{C}}^ n\), \(n\geq 2\), \(0\in D\), and let \(D_ m\), \(m=1,2,...\), be a sequence of convex bounded domains such that \(\bar D_ m\subset D_{m+1}\) and \(\cup^{\infty}_{m=1}D_ m=D\). Put \(H_ m(z)= \max (Re :\) \(\lambda \in \bar D_ m)\) where \(= \sum^{n}_{k=1} \lambda_ kz_ k\), and \(P_ D=\{f\)-entire ...
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Composition Operators on Hilbert Spaces of Entire Functions of Several Variables

Integral Equations and Operator Theory, 2017
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Minh Luan Doan, Le Hai Khoi, Trieu Le
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ON THE ADDITION OF THE INDICATORS OF ENTIRE AND SUBHARMONIC FUNCTIONS OF SEVERAL VARIABLES

Mathematics of the USSR-Sbornik, 1978
In this article a necessary and sufficient criterion is derived for a subharmonic function  defined in  and having proximate order  to belong to the class of functions of completely regular growth. The criterion is that for any subharmonic function  with the same proximate order the sum of the regularized indicators of  and  be equal to the regularized
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ON REPRESENTING ENTIRE FUNCTIONS OF SEVERAL VARIABLES BY DIRICHLET SERIES

Mathematics of the USSR-Sbornik, 1972
Let be an entire function of two complex variables. Let us take the proximate order and then define positive numbers () so that , . Let us choose an integer 2$ SRC=http://ej.iop.org/images/0025-5734/18/4/A04/tex_sm_1862_img7.gif/> and form the numbers (; ). Let () be arranged these numbers in the order of decreasing modulus.
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A UNICITY THEOREM FOR ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES

Chinese Annals of Mathematics, 2004
The author proves the following result: Let \(f\) and \(g\) be two nonconstant entire functions on \(\mathbb{C}^n\), and let \(k\) be a positive integer. If \(f\) and \(g\) share \(0\) CM, that is, \(f\) and \(g\) have the same zeros counting multiplicities, \(D^kf\) and \(D^kg\) share \(1\) CM, and if \(\delta(0,f)>1/2\), then \(f=g\).
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On periodic decomposition of entire functions of several variables

Aequationes mathematicae, 2014
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