On Domains of Convergence of Multidimensional Lacunary Series
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...
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| Veröffentlicht in: | Journal of Siberian Federal University. Mathematics & Physics 2019-01, Vol.12 (6), p.736-746 |
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| container_title | Journal of Siberian Federal University. Mathematics & Physics |
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| creator | Tuychiev, Taxir T. |
| description | 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 |
| doi_str_mv | 10.17516/1997-1397-2019-12-6-736-746 |
| format | Article |
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| identifier | ISSN: 1997-1397 |
| ispartof | Journal of Siberian Federal University. Mathematics & Physics, 2019-01, Vol.12 (6), p.736-746 |
| issn | 1997-1397 2313-6022 |
| language | eng |
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| source | Math-Net.Ru (free access) |
| subjects | Convergence Domains Polynomials Theorems |
| title | On Domains of Convergence of Multidimensional Lacunary Series |
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