A functional model associated with a generalized Nevanlinna pair

Abstract

Let L be a Hilbert space and let H be a Pontryagin space. For every selfadjoint linear relation à in H⊕L the pair {I+λψ(λ), ψ(λ)}, where ψ(λ) is the compressed resolvent of Ã, is a normalized generalized Nevanlinna pair. Conversely, every normalized generalized Nevanlinna pair is shown to be associated with some selfadjoint linear relation à in the above sense. A functional model for this selfadjoint linear relation à is constructed.