Directional logarithmic derivative and the distribution of zeros of an entire function of bounded $L$-index in the direction
We establish new criteria of boundedness of the $L$-index in the direction for entire functions in $C^n$. These criteria are formulated as estimate of the maximum modulus via the minimum modulus on a circle and describe the distribution of their zeros and the behavior of the directional logarithmic...
Збережено в:
| Дата: | 2017 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2017
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1706 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We establish new criteria of boundedness of the $L$-index in the direction for entire functions in $C^n$. These criteria are formulated as estimate of the maximum modulus via the minimum modulus on a circle and describe the distribution of their
zeros and the behavior of the directional logarithmic derivative. In this way, we prove Hypotheses 1 and 2 from the article
[Bandura A. I., Skaskiv O. B. Open problems for entire functions of bounded index in direction // Mat. Stud. – 2015. – 43,
№ 1. – P. 103 – 109]. The obtained results are also new for the entire functions of bounded index in $C$. They improve the
known results by M. N. Sheremeta, A. D. Kuzyk, and G. H. Fricke. |
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