Krein-Langer Factorizations via Pole Triples

Abstract.

A theorem by Krein and Langer asserts existence of factorizations of special type for operator functions in a generalized Schur class, i. e., meromorphic operator functions defined on the unit disk and such that their Nevanlinna-Pick kernel has a fixed finite number of negative squares. A different view and proof of this theorem are presented, based on description of pole data of meromorphic operator functions in terms of pole pairs and pole triples. A criterion for existence, and a parametrization, of operator functions in a generalized Schur class with given pole triple is obtained.