Description of sequences of zeros of one class of functions analytic in a half-plane

Abstract

We describe sequences of zeros of functions ƒ ≠ 0 that are analytic in the right half-plane and satisfy the condition ¦ƒ(z)¦ ≤ 0(1) exp (σ¦ z ¦η(¦ z ¦)), 0 ≤ <+ ∞, Re z > 0, where η: [0; + ∞) → (- ∞; + ∞) is a function of bounded variation.