ENTIRE FUNCTION OF UNBOUNDED INDEX IN ANY REAL DIRECTION
Keywords:
entire function, bounded L -index in direction, directional derivative, unbounded index in any direction.Abstract
We prove that an entire function $F( z_1 , z_2 ) = \cos\sqrt{z_1 z_2}$ is of unbounded
index in any complex direction b = (b 1 , b 2 ) ∈ C2 \ 0. But F ( z 1 0 + b 1t , z2 0 + t ) is
of bounded index for every given z 1 0 , z 2 0 as function of variable t. It is a
generalization of our previous result for direction (1,1).
References
1. Bandura A.I. Sufficient sets for boundedness L -index in direction for entire functions / A.I. Bandura, O.B. Skaskiv // Mat. Stud. – 2007. – 30, no 2. – P. 177-182.
2. Bandura A.I. Entire functions of bounded L -index in directionA.I. Bandura, O.B. Skaskiv // Mat. Stud. – 2007. – 27, no. 1. – P. 30-52 (in Ukrainian).
3. Bandura A.I. Entire functions of bounded and unbounded index in direction / A.I. Bandura, O.B. Skaskiv // Mat. Stud. – 2007. – 27, no. 2.P. 211-215 (Ukrainian).
4. Fricke G.H. On bounded value distribution and bounded index, Nonlinear Anal / G.H. Fricke, S.M. Shah. – 1978. – 2, no 4. – P. 423-435.
2. Bandura A.I. Entire functions of bounded L -index in directionA.I. Bandura, O.B. Skaskiv // Mat. Stud. – 2007. – 27, no. 1. – P. 30-52 (in Ukrainian).
3. Bandura A.I. Entire functions of bounded and unbounded index in direction / A.I. Bandura, O.B. Skaskiv // Mat. Stud. – 2007. – 27, no. 2.P. 211-215 (Ukrainian).
4. Fricke G.H. On bounded value distribution and bounded index, Nonlinear Anal / G.H. Fricke, S.M. Shah. – 1978. – 2, no 4. – P. 423-435.
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Published
2019-02-26
How to Cite
Бандура, А. І. (2019). ENTIRE FUNCTION OF UNBOUNDED INDEX IN ANY REAL DIRECTION. PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, (1(29), 24–30. Retrieved from https://pvntsh.nung.edu.ua/index.php/number/article/view/136
Issue
Section
Mathematics and Mechanics
