Partial logarithmic derivatives and distribution of zeros of analytic functions in the unit ball of bounded L-index in joint variables
We obtain the sufficient conditions of boundedness of L-index in joint variables for analytic functions in the unit ball, where L : Cⁿ → Rⁿ₊ is a continuous positive vector-function. They give an estimate of the maximum modulus of an analytic function by its minimum modulus on a skeleton in a polydi...
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| Veröffentlicht in: | Український математичний вісник |
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| Datum: | 2018 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/169396 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Partial logarithmic derivatives and distribution of zeros of analytic functions in the unit ball of bounded L-index in joint variables / A.I. Bandura, O.B. Skaskiv // Український математичний вісник. — 2018. — Т. 15, № 2. — С. 177-193. — Бібліогр.: 37 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We obtain the sufficient conditions of boundedness of L-index in joint variables for analytic functions in the unit ball, where L : Cⁿ → Rⁿ₊ is a continuous positive vector-function. They give an estimate of the maximum modulus of an analytic function by its minimum modulus on a skeleton in a polydisc and describe the behavior of all partial logarithmic derivatives outside some exceptional set and the distribution of zeros. The deduced results are also new for analytic functions in the unit disc of bounded index and l-index. They generalize known results by G. H. Fricke, M. M. Sheremeta, A. D. Kuzyk, and V. O. Kushnir.
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| ISSN: | 1810-3200 |