Geodesic
On domains of convergence of multidimensional lacunary series
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 6, pp. 736-746 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] E. Fabry, “Sur les points singuliers d'une fonction donnee par son developpement de Taylor”, Ann. ec. Norm. Sup. Paris, 13:3 (1896), 367–399 | DOI | MR | Zbl

[2] G. Faber, “Uber Potenzreihen mit unendlich vielen verschiedenen koeffizienten”, Sitzgsber. Bayr. Akad. Wiss., Mat.-nat. Abt., 1906, 581–583 | Zbl

[3] G. Polya, “Untersuchungen uber Luchen und Sungularitaten von potenzreihen”, Math. Z., 29 (1929), 549–640 | DOI | MR | Zbl

[4] J. Siciak, “Some gap power series in multidimensional setting”, Ann. Univ. Maria e Curie-Sklodowska Lublin-Polonia, 65:2 (2011), 179–190 | MR | Zbl

[5] A. Sadullaev, “Plurissubharmonic functions”, Current problems in mathematics. Fundamental directions, 8, VINITI, M., 1985, 65–113 (in Russian) | MR

[6] A. Sadullaev, Pluripotential theory. Applications, Palmarium academik publishing, Saarbruchen Deutschland, 2012 (in Russian)

[7] T. Tuychiev, A. Mardanov, “On domains of convergence of lacunary series with respect to homogeneous polynomials”, Uzbek Mathematical Journal, 2014, no. 1, 108–118 (in Russian) | MR

[8] M. Jarnicki, P. Pflug, Separately analytic functions, European Mathematical Society, 2011 | MR | Zbl

[9] A. Sadullaev, T. Tuychiev, “On the extension of the Hartogs series admitting a holomorphic extension to parallel sections”, Uzbek Mathematical Journal, 2009, no. 1, 148–157 (in Russian) | MR

[10] A. Kolmogorov, S. Fomin, Elements of the theory of functions and functional analysis, Nauka, M., 1976 (in Russian) | MR

[11] T. Tuychiev, “Continuation of functions along a fixed direction”, Sibirsk. math. journal, 29:3 (1988), 142–147 (in Russian) | MR

[12] T. Tuychiev, A. Mardanov, “On multidimensional analogues of the Fabry and Polya theorems for lacunary Hartogs series”, Uzbek Mathematical Journal, 2012, no. 3, 126–134 (in Russian) | MR

[13] B. Shabat, Introduction to the complex analysis, Nauka, M., 1985 (in Russian) | MR