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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.

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)