On Domains of Convergence of Multidimensional Lacunary Series

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
1. Verfasser: Tuychiev, Taxir T.
Format: Artikel
Sprache:eng
Schlagworte:
Convergence
Domains
Polynomials
Theorems
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Beschreibung
Zusammenfassung: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
ISSN:1997-1397
2313-6022
DOI:10.17516/1997-1397-2019-12-6-736-746