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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 142, Pages 88–101 (Mi into256)  

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.
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 241, Issue 6, Pages 735–749
DOI: https://doi.org/10.1007/s10958-019-04459-8
Bibliographic databases:
Document Type: Article
UDC: 517.55, 517.51
MSC: 32A15, 30C45
Language: Russian
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
Citation in format AMSBIB
\Bibitem{ZavMae17}
\by M.~N.~Zav'yalov, L.S.~Maergoiz
\paper Sketch of the theory of growth of functions holomorphic in a multidimensional torus
\inbook Complex analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 142
\pages 88--101
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into256}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801352}
\zmath{https://zbmath.org/?q=an:1426.32002}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 241
\issue 6
\pages 735--749
\crossref{https://doi.org/10.1007/s10958-019-04459-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85070265678}
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