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.

Keywords

• symmetric operator
• selfadjoint extension
• boundary relation
• Weyl family
• functional model
• reproducing kernel Hilbert space