关键词: N[WTBX](E\-m)函数类, NP(N(E_m))问题, 广义Stieltjes矩量

Abstract:

Let E\-m=(-∞,∞)＼∪[DD(]m[]j=1[DD)](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.

Key words: N(E_m) class, NP(N(E_m)) problem, Generalized Stieltjes moment problem, Hankel vector