Abstract
A mixed type, Lowner and Nevanlinna-Pick directional two-sided interpolation problem is considered. A necessary and sufficient condition for the problem to have a solution is established, in terms of properties of the Pick kernel to the problem. As well, a parametrization of the set of all real rational solutions of minimal degree is given. The corresponding Nevanlinna-Pick boundary-interior interpolation problem is also considered and a solvability condition for it is obtained. The approach to the problem is via functional Hilbert spaces.
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