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.
- 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
- Received: 2008-03-31.
- Accepted: 2008-04-14.
