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Characteristics of the sum of a multidimensional series

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Ukrainian Mathematical Journal Aims and scope

Abstract

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 σ Qβ(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.

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References

  1. V. P. Gromov, “About the theory of repeating Dirichlet series. I,”Sci. Papers Acad. Sci. Armenian SSR, Mathematics, No. 5, 449–458 (1970).

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Authors and Affiliations

  1. Bryansk Pedagogical Institute, Bryansk

    V. Yu. Makarov

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  1. V. Yu. Makarov
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Published in Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 7, pp. 886–892, July, 1994.

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Makarov, V.Y. Characteristics of the sum of a multidimensional series. Ukr Math J 46, 971–978 (1994). https://doi.org/10.1007/BF01056674

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  • DOI: https://doi.org/10.1007/BF01056674

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