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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 142, Pages 88–101
(Mi into256)
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Sketch of the theory of growth of functions holomorphic in a multidimensional torus
M. N. Zav'yalov, L.S. Maergoiz Siberian Federal University, Krasnoyarsk
Abstract:
We develop an approach to the theory of growth of class-$H(\mathbb{T}^n)$ functions holomorphic in a multidimensional torus $\mathbb{T}^n$ based on the structure of elements of this class and well-known results of the theory of growth of entire functions of several complex variables. This approach is illustrated in the case where the growth of the function $g\in H(\mathbb{T}^n)$ is compared with the growth of its maximum modulus on the skeleton of polydisk. Properties of the corresponding characteristics of growth of class-$H(\mathbb {T}^n)$ functions are examined and their relation to coefficients of their Laurent series are studied. A comparative analysis of these results and similar assertions of the theory of growth of entire functions of several variables is given.
Keywords:
entire function of several variables, holomorphic function in multidimensional torus, convex function, characteristics of growth, multiple Laurent series, carrier, strictly convex cone.
Citation:
M. N. Zav'yalov, L.S. Maergoiz, “Sketch of the theory of growth of functions holomorphic in a multidimensional torus”, Complex analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 142, VINITI, M., 2017, 88–101; J. Math. Sci. (N. Y.), 241:6 (2019), 735–749
Linking options:
https://www.mathnet.ru/eng/into256 https://www.mathnet.ru/eng/into/v142/p88
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