### 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 : ℂ

^{n}→ 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 ℂ

^{n}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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