Functional models for Nevanlinna families

Abstract

The class of Nevanlinna families consists of $\mathbb{R}$-symmetric holomorphic multivalued functions on $\mathbb{C} \setminus \mathbb{R}$ with maximal dissipative (maximal accumulative) values on $\mathbb{C}{+}$ ($\mathbb{C}{-}$, respectively) and is a generalization of the class of operator-valued Nevanlinna functions. In this note Nevanlinna families are realized as Weyl families of boundary relations induced by multiplication operators with the independent variable in reproducing kernel Hilbert spaces.