2019
Том 71
№ 2

All Issues

On zeros of functions of given proximate formal order analytic in a half-plane

Sharan V.L., Vynnyts’kyi B. V.

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Abstract

We describe sequences of zeros of functionsf≢0 that are analytic in the half-plane ℂ+={z:Rez> and satisfy the condition $$\forall \varepsilon > 0\exists c_1 \in (0; + \infty )\forall z \in \mathbb{C}_{\text{ + }} :\left| {f(z)} \right| \leqslant c_1 \exp \left( {(\sigma + \varepsilon )\left| z \right|\eta (\left| z \right|)} \right)$$ where 0≤σ<+∞ and η is a positive function continuously differentiable on [0; +∞) and such thatxη′(x)/η(x)→0 asx→+∞.

English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 7, pp 1013-1019.

Citation Example: Sharan V.L., Vynnyts’kyi B. V. On zeros of functions of given proximate formal order analytic in a half-plane // Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 904–909.

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