Operator Models for Meromorphic Functions of Bounded Type

It has been known for a long time that cyclic self-adjoint operators on Hilbert spaces correspond to Herglotz-Nevanlinna functions, and that the corresponding function encodes the spectral properties of the underlying operator. This result was extended by Krein and Langer in the 1970s, who showed that cyclic self-adjoint operators on Pontryagin spaces correspond to generalized Nevanlinna function. In this talk, we prove that meromorphic functions of bounded type correspond to a certain subclass of rank-one perturbations of self-adjoint operators on Hilbert spaces, which is done using Model Space theory.