On the similarity of boundary triples of symmetric operators in Krein spaces

TL;DR

This paper extends the classical correspondence between Weyl functions and boundary triples from symmetric operators in Hilbert spaces to those in Pontryagin spaces, using similarity instead of unitary equivalence.

Contribution

It generalizes the uniqueness of boundary triples determined by Weyl functions to the setting of Pontryagin spaces, replacing unitary equivalence with similarity.

Findings

Weyl function determines boundary triples up to similarity in Pontryagin spaces

Extension of classical Hilbert space results to indefinite inner product spaces

Provides a framework for analyzing symmetric operators in Krein spaces

Abstract

It is a classical result that the Weyl function of a simple symmetric operator in a Hilbert space determines a boundary triple uniquely up to unitary equivalence. We generalize this result to a simple symmetric operator in a Pontryagin space, where unitary equivalence is replaced by the similarity realized via a standard unitary operator.