N(E_m)函数类中Nevanlinna-Pick插值与相关的广义Stieltjes矩量问题  

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

作　　者：吴化璋[1] 

机构地区：[1]安徽大学数学系

出　　处：《数学物理学报（A辑）》2004年第4期385-394,共10页Acta Mathematica Scientia

基　　金：国家自然科学基金(10271113)安徽省教育厅(2003kj024)基金资助

摘　　要：令 .函数类N(E_m)表示在上半复平面解析且虚部非负,在诸(αj,βj)(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N(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Em上非标准截断广义Stieltjes矩量问题的可解性准则,从而获得了N(E_m)函数类中Nevanlinna-Pick问题的可解性准则.Let . The author denotes by N(Em) the class of allfunctions which are holomorphic in the upper half-plane and whose imaginary parts are nonnegative, and which are holomorphic and take real values on each interval (αj,βj)(j= 1,...,m). In this paper an one-to-one correspondence between the solutions to the Nevan linna-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.

关 键 词：N(Em)函数类 NP(N(Em))问题 广义Stieltjes矩量问题 Hankel向量 

分 类 号：O174.42[理学—数学] O174.43[理学—基础数学]