2019
Том 71
№ 11

All Issues

Minimum of modulus of dirichlet multisequence

Lutsyshyn M. R., Skaskiv O. B.

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Abstract

Conditions are established under which the following relation is satisfied: $$M(x) = (1 + o(1))m(x) = (1 + o(1))\mu (x)$$ as $|x |→ + ∞$ outside a sufficiently small set, for an entire function $F(z)$ of several complex variables $z ∈ ℂ_p,p ≥ 2$, represented by a Dirichlet series. Here $M(x) = \sup \{|F(x+iy) |: y ∈ ℝ^p\}$ and $m(x) = \inf \{ |F(x+iy) |:y ∈ ℝ^p,$ with $μ(x)$ the maximal term of the Dirichlet series, $x ∈ ℝ^p$.

English version (Springer): Ukrainian Mathematical Journal 44 (1992), no. 9, pp 1186–1188.

Citation Example: Lutsyshyn M. R., Skaskiv O. B. Minimum of modulus of dirichlet multisequence // Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1295–1297.

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