2019
Том 71
№ 9

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Characteristics of the sum of a multidimensional series

Makarov V. Yu.

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Abstract

We study the relationship between the asymptotic behavior of 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. Growth characteristics, an order $\rho_Q(a)$, and a type $\sigma_{Q \beta}(a)$ in an octant $Q(a)$ are determined. The dependence of growth characteristics on the coordinates of points of the boundary of the domain of convergence is established.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 7, pp 971-978.

Citation Example: Makarov V. Yu. Characteristics of the sum of a multidimensional series // Ukr. Mat. Zh. - 1994. - 46, № 7. - pp. 886–892.

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