Minimal realizations of generalized Nevanlinna functions

Abstract

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.

Keywords

• generalized Nevanlinna functions
• selfadjoint (multi-valued) operators
• (minimal) realizations