About some problem for entire functions of unbounded index in any direction
Journal Title: Математичні Студії - Year 2019, Vol 51, Issue 1
Abstract
In this paper, we select a class of entire functions F(z1,…,zn) such that for any direction (b1,…,bn)∈Cn∖{0} and for every point (z01,…,z0n)∈C the function F(z01+tb1,…,z0n+tbn) is of bounded index as a function in variable t∈C, but the function F is of unbounded index in every direction (b1,…,bn). This result partially solves Problem 18 from the article A. I. Bandura, O. B. Skaskiv, Open problems for entire functions of bounded index in direction, Mat. Stud., 43 (2015), no.1, 103–109. This problem concerns with existence of entire functions of unbounded L-index in any direction, where L:Cn→R+ is a continuous function and n≥3. Our result solves the problem in the case L≡1.
Authors and Affiliations
I. M. Hural
Keywords
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- EP ID EP584911
- DOI 10.15330/ms.51.1.107-110
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