Multiple Nevanlinna-Pick interpolation with both interior and boundary data and its connection with the power moment problem

The so-called Hankel vector approach is used to handle three boundary versi ons of the multiple Nevanlinna-Pick interpolation problem in the Nevanlinna class N involving both interior and boundary data. It turns out that each of these boundary interpolation problems can be reduced to what amounts to a certain truncated (standard or nonstandard) Hamburger moment problem, ass ociated with the Hankel vector of the former, with some possible constraint on distribution functions that assign no mass to any of the real nodes. In particular, this leads to solvability criteria for each of these interpola tion problems and the description of solutions by using results from theory of moments. (C) 2001 Elsevier Science Inc. All rights reserved. AMS classi fication: 30E05; 47A57: 15A57.