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On the proximate growth function relative to the model growth function
M. V. Kabankoa, K. G. Malyutina, B. N. Khabibullinb a Kursk State University
b Institute of Mathematics and Computing Centre of Ural Branch of Russian Academy of Sciences
Abstract:
The concept of proximate order is widely used in the theories of integer, meromorphic, subharmonic, and plurisubharmonic functions. In this paper, we provide a general interpretation of this concept as a proximate growth function relative to the model growth function. The classical proximate order is the proximate order in the sense of Valiron. Our definition uses only one condition. This form of definition is new for the classical proximate order. In this review, we show that for any function defined on a positive ray whose growth is determined by a model growth function, there is a proximate growth function relative to the model growth function.
Keywords:
Hadamard problem, model growth function, proximate order, convex function, entire function, subharmonic function.
Citation:
M. V. Kabanko, K. G. Malyutin, B. N. Khabibullin, “On the proximate growth function relative to the model growth function”, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 230, VINITI, Moscow, 2023, 56–74
Linking options:
https://www.mathnet.ru/eng/into1245 https://www.mathnet.ru/eng/into/v230/p56
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Abstract page: | 96 | Full-text PDF : | 31 | References: | 30 |
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