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Minimal realizations of generalized Nevanlinna functions

Hassi S., Wietsma H. L.

Opuscula Mathematica

2016

Vol. 36, no. 6

749--768

Minimal realizations of generalized Nevanlinna functions that carry the information on their generalized poles of nonpositive type in an explicit form are established. These realizations are based on a modification of the basic canonical factorization of generalized Nevanlinna functions whereby the non-minimality problems in realizations that are based directly on the canonical factorization are circumvented.

Functional models for Nevanlinna families

Behrndt J., Hassi S., Snoo H. de

Opuscula Mathematica

2008

Vol. 28, no. 3

233-245

The class of Nevanlinna families consists of R-symmetric holomorphic multivalued functions on C \ R with maximal dissipative (maximal accumulative) values on C+ (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.