Interpolation Problems with Null and Pole Pairs

Abstract

In Part I we were considering interpolation problems with standard combinations of the data. There we considered interpolation problems with given right null pair and left pole pair; the analogous interpolation problem where a left null pair and right pole pair are given can be reduced to the previous one by taking transpose. In this chapter we consider the interpolation problems for the remaining nonstandard combinations, namely the case where a null pair and pole pair from the same side are given. This problem differs considerably from the case of standard local data, both the procedure to find a solution and also in the properties of the solution. We also consider in this chapter the problem of interpolation when all four pairs (right and left null pair, right and left pole pair) are given. This problem can be regarded as an overdetermined version of the problem with standard data.