Opuscula Math. 28, no. 3 (2008), 233-245

Opuscula Mathematica

# Functional models for Nevanlinna families

Jussi Behrndt
Seppo Hassi
Henk de Snoo

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.

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• Jussi Behrndt
• Technische Universität Berlin, Institut für Mathematik, MA 6-4, Strasse des 17. Juni 136, 10623 Berlin, Deutschland
• Seppo Hassi
• University of Vaasa, Department of Mathematics and Statistics, P.O. Box 700, FI-65101 Vaasa, Finland
• Henk de Snoo
• University of Groningen, Department of Mathematics and Computing Science, P.O. Box 407, 9700 AK Groningen, Nederland