E_m函数类中Nevanlinna-Pick插值与广义Stieltjes矩量问题

令E\-m=(-∞,∞)＼∪DD(]m]j=1DD)](α\-j,β\-j).函数类WTHT]NWTBX](E\-m)表示在上半复平面解析且虚部非负,在诸(α\-j,β\-j)(j=1,…,m)内解析且为实值的函数全体.该文用Hankel 向量方法建立WTHT]NWTBX](E\-m)函数类 中含有限(或无限可数)插值点的Nevanlinna Pick 问题与集合E\-m上 相关的非标准截断(或全)广义Stieltjes 矩量问题解集之间的一一对应.用类似于Riesz的办法建立E\-m上非标准截断广义Stieltjes矩量问题的可解性准则,从而获得了WTHT]NWTBX](E\-m)函数类中Nevanlinna Pick问题的可解性准则.

The Nevanlinna-Pick Interpolation in the Class N(Em) and the Associated Generalized Stieltjes Moment Problem

Let E\-m=(-∞,∞)＼∪DD(]m]j=1DD)](α\-j,β\-j). The author denotes by N(E_m) the class of all functions which e holomorphic in the upper half plane and whose imaginary parts are nonnegative, and which are holomorphic and take real values on each  interval (α\-j,β\-j)(j=1,…,m).In this paper an one to one correspondence between the solutions to the  Nevanlinna Pick interpolation problem with finite(infinite) nodes  and the solutions to the associated nonstandard truncated(full) generalized Stieltjes moment problem is established by using Hankel vector approach. The solvability criteria for the  nonstandard truncated generalized Stieltjes moment problem and the corresponding Nevanlinna Pick  problem are  obtained by the  method due to Risez. Using the limiting  process, the author deduces the necessary condition  for  the solvable Nevanlinna Pick problem with infinite interpolation nodes.