Sketch of the Theory of Growth of Holomorphic Functions in a Multidimensional Torus : научное издание


Тип публикации: статья из журнала

Год издания: 2019

Ключевые слова: 30C45, 32A15, carrier, characteristics of growth, convex function, entire function of several variables, holomorphic function in multidimensional torus, Multiple Laurent series, strictly convex cone

Аннотация: We develop an approach to the theory of growth of the class H(𝕋n) of holomorphic functions in a multidimensional torus 𝕋n 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 fПоказать полностьюunction g ∈ H(𝕋n) 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(𝕋n) 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.

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Журнал: Journal of Mathematical Sciences

Выпуск журнала: Т. 241, 6

Номера страниц: 735-749

ISSN журнала: 10723374

Место издания: Москва

Издатель: Plenum Publishers


  • Zavyalov M.N. (Siberian Federal University)
  • Maergoiz L.S. (Federal Research Center “Krasnoyarsk Science Center of the Siberian Branch of the Russian Academy of Sciences”)

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