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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)