Solvability condition for a boundary value interpolation problem of Loewner type (Q1128167)

Let \(E\) be a finite subset of the real numbers. The interpolation problem considered here is to find a holomorphic function on the upper half plane with a nonnegative imaginary part and with prescribed radial residue and first several radial pseudo-derivatives at each point of \(E\). A necessary and sufficient condition is found for the solvability of this problem in terms of the Pick matrix. The author also obtains a parametrization of the set of solutions in the spirit of the classical Nevanlinna parametrization. This result extends a previous one by the author [Interpolation problems of Loewner type with finitely many nodes (to appear)].