Operator models for meromorphic functions of bounded type

Abstract

In this article, we construct operator models for meromorphic functions of bounded type on Krein spaces. This construction is based on certain reproducing kernel Hilbert spaces which are closely related to model spaces. Specifically, we show that each function of bounded type corresponds naturally to a pair of such spaces, extending Helson's representation theorem. This correspondence enables an explicit construction of our model, where the Krein space is a suitable sum of these identified spaces. Additionally, we establish that the representing self-adjoint relations possess a relatively simple structure, proving to be partially fundamentally reducible. Conversely, we show that realizations involving such relations correspond to functions of bounded type.