A class of entire functions of unbounded index in each direction

Author
A. I. Bandura
Department of higher mathematics, Ivano-Frankivs’k National Technical University of Oil and Gas
Abstract
We select a class of entire functions $f(z_1,z_2)$ with the property $\forall \mathbf{b}=(b_1,b_2)\in\mathbb{C}^2\setminus\{0\}$ $\forall~z_1^0,$ $z_2^0\in\mathbb{C}$ the function $f(z_1^0+tb_1,z_2^0+tb_2)$ is of bounded index as a function in variable $t\in\mathbb{C},$ but $f(z_1,z_2)$ is of unbounded index in every direction $\mathbf{b}.$ Thus, it solves Problem 17 from the article A. I. Bandura, O. B. Skaskiv, {\it Open problems for entire functions of bounded index in direction,} Mat. Stud., \textbf{43} (2015), no.1, 103--109.
Keywords
entire functions of two variables; unbounded index in direction; directional derivative
DOI
doi:10.15330/ms.44.1.107-112
Reference
1. A.I. Bandura, O.B. Skaskiv, Entire functions of bounded L-index in direction, Mat. Stud., 27 (2007), ¹1, 30–52. (in Ukrainian)

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4. A.I. Bandura, O.B. Skaskiv, Open problems for entire functions of bounded index in direction, Mat. Stud., 43 (2015), ¹1, 103–109. dx.doi.org/10.15330/ms.43.1.103–109.

5. A.I. Bandura, O.B. Skaskiv, Entire functions of several variables of bounded L-index in direction and of bounded L-index in joint variables. https://arxiv.org/abs/1508.07486.

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Pages
107-112
Volume
44
Issue
1
Year
2015
Journal
Matematychni Studii
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