Coupling of definitizable operators in Krein spaces
Indefinite Sturm-Liouville operators defined on the real line are often considered as a coupling of two semibounded symmetric operators defined on the positive and the negative half axis. In many situations, those two semibounded symmetric operators have in a special sense good properties like a Hilbert space self-adjoint extension. In this paper we present an abstract approach to the coupling of two (definitizable) self-adjoint operators. We obtain a characterization for the definitizability and the regularity of the critical points. Finally we study a typical class of indefinite Sturm-Liouville problems on the real line.
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