Sketch of the Theory of Growth of Holomorphic Functions in a Multidimensional Torus

We develop an approach to the theory of growth of the class H (𝕋 n ) of holomorphic functions in a multidimensional torus 𝕋 n based on the structure of elements of this class and well-known results of the heory of growth of entire functions of several complex variables. This approach is illustrated...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) Vol. 241; no. 6; pp. 735 - 749
Main Authors: Zavyalov, M. N., Maergoiz, L. S.
Format: Journal Article
Language:English
Published: New York Springer US 09.09.2019
Springer
Subjects:
Mathematics
Mathematics and Statistics
32A15
carrier
30C45
multiple Laurent series
convex function
strictly convex cone
entire function of several variables
holomorphic function in multidimensional torus
characteristics of growth
ISSN:1072-3374, 1573-8795
Online Access:Get full text
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Summary:We develop an approach to the theory of growth of the class H (𝕋 n ) of holomorphic functions in a multidimensional torus 𝕋 n based on the structure of elements of this class and well-known results of the heory of growth of entire functions of several complex variables. This approach is illustrated in the case where the growth of the function g ∈ H (𝕋 n ) is compared with the growth of its maximum modulus on the skeleton of the polydisk. The properties of the corresponding characteristics of growth of the functions in the class H (𝕋 n ) are studied with their relation to coefficients of the corresponding Laurent series. A comparative analysis of these results and similar assertions of the theory of growth of entire functions of several variables is given.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04459-8