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

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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→+∞.

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Authors
  1. B. V. Vinnitskii
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  2. V. L. Sharan
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Additional information

Drohobych Pedagogic University, Drohobych. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 7, pp. 904–909, July, 1999.

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Vinnitskii, B.V., Sharan, V.L. On zeros of functions of given proximate formal order analytic in a half-plane. Ukr Math J 51, 1013–1019 (1999). https://doi.org/10.1007/BF02592037

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  • DOI: https://doi.org/10.1007/BF02592037

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