Abstract

The aim of this paper is to study the multiple interpolation problem in the spaces of analytical functions of finite order \(\rho>1\) in the half-plane. The necessary and sufficient conditions for solvability of interpolation problem are obtained. These conditions are obtained in terms of the Nevanlinna product of interpolation nodes. 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.

中文翻译：

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半平面有限阶函数的多重插值

摘要

本文的目的是研究半平面有限阶\（\ rho> 1 \）的解析函数空间中的多重插值问题。获得了插值问题可解性的充要条件。这些条件根据插值节点的Nevanlinna乘积获得。内插问题的解决方案以Jones内插序列的形式构造，这是Lagrange内插序列的推广。