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

We describe sequences of zeros of functions f ≢ 0 that are analytic in the right half-plane and satisfy the condition {pipe}f(z){pipe} ≤ O(1) exp (σ{pipe} z {pipe}η({pipe} z {pipe})), 0 ≤ σ <+ ∞, Rez > 0, where η: [0; + ∞) → (- ∞; + ∞) is a function of bounded variation. © 1999 Kluwer Academic/Plenum Publishers.