Multiple Nevanlinna–Pick interpolation with both interior and boundary data and its connection with the power moment problem Original Research Article

The so-called Hankel vector approach is used to handle three boundary versions of the multiple Nevanlinna–Pick interpolation problem in the Nevanlinna class image 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, associated 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 interpolation problems and the description of solutions by using results from theory of moments.