2017
Том 69
№ 9

All Issues

On Zeros of One Class of Functions Analytic in a Half-Plane

Sharan V.L., Vynnyts’kyi B. V.

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Abstract

We describe sequences of zeros of functions f ≢ 0 analytic in the half-plane \({\mathbb{C}}_ + = \{ z:\operatorname{Re} z >0\}\) and satisfying the condition \((\exists {\tau}_1 \in (0;1))(\exists c_1 >0)(\forall z \in {\mathbb{C}}_ + ):|f(z)| \leqslant c_1 \exp ({\eta}^{\tau }_1 (c_1 |z|)),\) where η: [0; +∞) → (0; +∞) is an increasing function such that the function ln η(r) is convex with respect to ln r on [1; +∞).

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 9, pp 1514-1521.

Citation Example: Sharan V.L., Vynnyts’kyi B. V. On Zeros of One Class of Functions Analytic in a Half-Plane // Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1254-1259.

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