An Operator Theoretic Approach to Degenerated Nevanlinna‐Pick Interpolation

In this paper we consider an interpolation problem of Nevanlinna-Pick type: If finitely many points z1, . . . , zn of the open upper half plane C + are given, we study the existence of functions f ∈ Nν assuming prescribed values w1, . . . , wn ∈ C in these points: f(zi) = wi for i = 1, . . . , n. (1) Furthermore a description of all solutions of (1) through selfadjoint extensions of a certain symmetric operator is given. We recall the definition of the classes Nν . If f is a complex function denote by ρ(f) the domain of holomorphy of f . Definition 1 Let π and ν be nonnegative integers or ∞. Denote by Nν the set of all functions f which are meromorphic in C, such that the kernel