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

Abstract

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.