On Domains of Convergence of Multidimensional Lacunary Series
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https://elib.sfu-kras.ru/handle/2311/127027Author:
Tuychiev, Taxir T.
Туйчиев, Тахир Т.
Date:
2019-12Journal Name:
Журнал Сибирского федерального университета. Математика и физика. Journal of Siberian Federal University. Mathematics & Physics; 2019 12 (6)Abstract:
This paper is devoted to multidimensional analogues of the Fabry and P˙olya theorems on lacunary series.
Domains of convergence of lacunary Hartogs series and series in homogeneous polynomials are studied
in this paper. Analogues of the Fabry and P˙olya theorems for such series are given and domains of
convergence of these series are described. Results of the work develop well-known result of J. Siciak on
the domain of convergence of the lacunary series with respect to homogeneous polynomials Данная работа посвящена многомерным аналогам теорем Фабри и Полиа о лакунарных рядах.
В работе исследуются области сходимости лакунарных рядов Хартогса и рядов по однородным
полиномам. Приводятся аналоги теорем Фабри и Полиа для таких рядов и описываются области сходимости этих рядов. Также развивается известный результат Й.Сичака об областях
сходимости лакунарных рядов по однородным полиномам
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