On Interpolation Sequences of One Class of Functions, Analytic in the Half-Plane

Abstract

A new criterion of solvability of the interpolation problem f(λ _n )=b_n in the class of functions f, analytic in the right half-plane $\mathbb{C}_ +$ and such that there exists c ₁∈(0;+∞) such that |f(z)|≤c ₁exp(η(c₁|z|)) for all z ∈$\mathbb{C}_ +$, where η is a positive increasing continuous differentiable function on [0;+∞), for which η(t)→+∞ as t→+∞ and there exists c ₂∈(0;+∞) such that

$$\frac{{\eta (t)\ln \eta (t)}}{{t\eta '(t)}} \leqslant c_2 $$

for all t≥ 1 is described.