Boundedness of $\mathbf{L}$-Index in Joint Variables for Sum of Entire Functions
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Authors: A. BANDURA
DOI: 10.46793/KgJMat2204.595B
Abstract:
In the paper, we present sufficient conditions of boundedness of L-index in joint variables for a sum of entire functions, where L : ℂn → ℝ+n is a continuous function, ℝ+ = (0, +∞). They are applicable to a very wide class of entire functions because for every entire function F in ℂn with bounded multiplicities of zero points there exists a positive continuous function L such that F has bounded L-index in joint variables. Our propositions are generalizations of Pugh’s result obtained for entire functions of one variable of bounded index.
Keywords:
Entire function of several variables, bounded L-index in joint variables, sum of entire functions.
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