Ukrainian Mathematical Journal

, Volume 46, Issue 7, pp 971–978 | Cite as

Characteristics of the sum of a multidimensional series

  • V. Yu. Makarov


We study the correlation between the asymptotic behavior of the coefficients of a multidimensional series of exponents and the asymptotic behavior of its sum near a point on the boundary of the domain of convergence. The order ρQ(a) and the type σQβ(a) of growth in an octantQ (a) are determined. The dependence of the growth characteristics on the coordinates of points of the boundary of the convergence domain is established.


Asymptotic Behavior Growth Characteristic Convergence Domain Multidimensional Series 
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  1. 1.
    V. P. Gromov, “About the theory of repeating Dirichlet series. I,”Sci. Papers Acad. Sci. Armenian SSR, Mathematics, No. 5, 449–458 (1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • V. Yu. Makarov
    • 1
  1. 1.Bryansk Pedagogical InstituteBryansk

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