Geodesic
On domains of convergence of multidimensional lacunary series
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 6, pp. 736-746

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This paper is devoted to multidimensional analogues of the Fabry and Pȯlya 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 Pȯlya 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.
Keywords: plurisubharmonic function, singular point, negligible sets in $\mathbb{C}^{n}$, power series, lacunar Hartogs series, series in homogeneous polynomials. 
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     author = {Taxir T. Tuychiev},
     title = {On domains of convergence of multidimensional lacunary series},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {736--746},
     publisher = {mathdoc},
     volume = {12},
     number = {6},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a9/}
}
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Taxir T. Tuychiev. On domains of convergence of multidimensional lacunary series. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 6, pp. 736-746. http://geodesic.mathdoc.fr/item/JSFU_2019_12_6_a9/