On New and Earlier Developments in Petrenko’s Theory of Growth of Meromorphic Functions
Petrenko's theory of growth of meromorphic functions lies within the wider spectrum of Nevanlinna theory and was initiated by V.P. Petrenko in 1960s. This paper is focused on the achievements of an outstanding student of V.P. Petrenko, I.I. Marchenko, and his contributions to the theory. An ove...
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| Date: | 2025 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1114 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | Petrenko's theory of growth of meromorphic functions lies within the wider spectrum of Nevanlinna theory and was initiated by V.P. Petrenko in 1960s. This paper is focused on the achievements of an outstanding student of V.P. Petrenko, I.I. Marchenko, and his contributions to the theory. An overview of some of I.I. Marchenko's main results (and their further generalizations and applications) concerning deviations, separated maximum modulus points and strong asymptotic values constitutes the body of the paper. The final part of the paper is devoted to a generalization of an early result of I.I. Marchenko and A.I. Shcherba on the sum of deviations of functions holomorphic in the unit disc.
Mathematical Subject Classification 2020: 30D35, 30D30 |
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