Interpolation sets in spaces of functions of finite order in half–plane

We consider free interpolation problems, the study of which was initiated by A.F. Leontiev. We obtain new criterions for the interpolation property of sets in the space of analytic in the upper half–plane functions of finite order. We provide examples of interpolation sets in the space of analytic in the upper half–plane functions of finite order. These examples are similar to interpolation sets in the space of analytic and bounded in the upper half–plane functions. In particular, we provide examples of sets satisfying the Newman condition and uniform Frostman condition.