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Functional models for Nevanlinna families. (English) Zbl 1183.47004
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 paper, Nevanlinna families are realized as Weyl families of boundary relations induced by multiplication operators with the independent variable in reproducing kernel Hilbert spaces.

MSC:
47A20 Dilations, extensions, compressions of linear operators
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
47B25 Linear symmetric and selfadjoint operators (unbounded)
47B32 Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
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