Problem of multiple interpolation in class of analytical functions of zero order in half-plane

Abstract

In the paper we consider the problem of multiple interpolation in a class of functions of a zero order and type not exceeding normal in the upper half-plane of the complex variable. This problem belongs to the class of problems of free interpolation considered initially by A.F. Leont'ev. We find necessary and sufficient solvability conditions for this problem. The found criteria are formulated in terms of the canonical products constructed on interpolation nodes, and in terms of the Nevanlinna measure determined by these nodes. The work is a continuation of researches of the second author considered similar problems in classes of analytic functions in the upper half-plane of a nonzero order.