On the negative squares of indefinite Sturm–Liouville operators

The number of negative squares of all self-adjoint extensions of a simple symmetric operator of defect one with finitely many negative squares in a Krein space is characterized in terms of the behaviour of an abstract Titchmarsh–Weyl function near 0 and ∞. These results are applied to a large class of symmetric and self-adjoint indefinite Sturm–Liouville operators with indefinite weight functions.