The interpolation problem in the spaces of analytical functions of finite order in the half-plane

Abstract

The aim of this paper is to study the interpolation problem in the spaces of analytical functions of finite order ρ > 1 in the half-plane. The necessary and sufficient conditions for its solvability in terms of the canonical Nevanlinna product of nodes of interpolation are obtained. The solution of the interpolation problem is constructed in the form of the Jones interpolation series, which is a generalization of the Lagrange interpolation series.