Ukrainian Mathematical Journal

, Volume 43, Issue 2, pp 246–249 | Cite as

Properties of exponential series, the exponents of which have finite density

  • E. K. Kurtigolova


Conditions are presented for the summability by the Abel method of exponential series with complex exponents, having finite angular density at the noncorner points of the boundary of the convex polygonal domain of convergence of the series; conditions are established for the convergence of these series at the points indicated above.


Polygonal Domain Finite Density Exponential Series Angular Density Complex Exponent 
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Literature cited

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    Yu. I. Mel'nik and E. K. Krutigolova, “The properties of certain special exponential series with compelx exponents,” Ukr. Mat. Zh.,41, No. 4, 571–573 (1989).Google Scholar
  2. 2.
    V. K. Dzyadyk and E. K. Krutigolova, “The representation of analytic functions by Dirichlet series on the boundary of the domain of convergence,” Mat. Zametki,14, No. 6, 769–784 (1973).Google Scholar
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    A. F. Leont'ev, Series of Exponents [in. Russian], Nauka, Moscow (1976).Google Scholar
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    Yu. I. Mel'nik, “A question on representing regular functions by Dirichlet series,” Mat. Zametki,21, No. 5, 54–65 (1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • E. K. Kurtigolova
    • 1
  1. 1.Drogobych Pedagogical InstituteUSSR

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