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...
Gespeichert in:
| Datum: | 2017 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2017
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1706 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
|---|