THE METRIC PROPERTIES OF A SPACE OF ENTIRE FUNCTIONS OF BOUNDED L -INDEX IN DIRECTION
Keywords:
entire function, bounded L -index in direction, bounded value L -distribution in direction, directional derivative.Abstract
The metric properties of a space of entire functions of bounded L - index in direction are investigated. It is shown that the space of entire functions with L -index in direction less than p is of the first category in the topology generated of Iyer's metric.
References
1. Ekblaw K.A. The functions of bounded index as a subspace of a space of entire functions / K.A.Ekblaw // Pacific J. Math. – 1971. – V.37. – P. 353-355.
2. Bordulyak M.T. The space of entire in Cn functions of bounded L -indexM.T.Bordulyak // Math. Stud. – 1995. – V.4. – P. 53-58 (in Ukrainian).
3. Bandura A.I. Entire functions of bounded L -index in directionA.I.Bandura, O.B.Skaskiv // Math. Stud. – 2007. – 27, N.1. – P. 30-52 (in Ukrainian).
4. Sheremeta M. Analytic functions of bounded index / M.Sheremeta // Sheremeta Myroslav. – Lviv: VNTL Publishers, 1999. – 141 p.
2. Bordulyak M.T. The space of entire in Cn functions of bounded L -indexM.T.Bordulyak // Math. Stud. – 1995. – V.4. – P. 53-58 (in Ukrainian).
3. Bandura A.I. Entire functions of bounded L -index in directionA.I.Bandura, O.B.Skaskiv // Math. Stud. – 2007. – 27, N.1. – P. 30-52 (in Ukrainian).
4. Sheremeta M. Analytic functions of bounded index / M.Sheremeta // Sheremeta Myroslav. – Lviv: VNTL Publishers, 1999. – 141 p.
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Published
2019-03-07
How to Cite
Bandura, A. I. (2019). THE METRIC PROPERTIES OF A SPACE OF ENTIRE FUNCTIONS OF BOUNDED L -INDEX IN DIRECTION. PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, (1(17), 113–119. Retrieved from https://www.pvntsh.nung.edu.ua/index.php/number/article/view/237
Issue
Section
Mathematics and Mechanics
