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
  • Received: 2008-03-31.
  • Accepted: 2008-04-14.
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Cite this article as:
Jussi Behrndt, Seppo Hassi, Henk de Snoo, Functional models for Nevanlinna families, Opuscula Math. 28, no. 3 (2008), 233-245

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