Opuscula Math.
28
, no. 3
(), 233-245
Opuscula Mathematica

# 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.
Mathematics Subject Classification: 47A20, 47A56, 47B25, 47B32.