Main Properties of the Faddeev Equation for 2 × 2 Operator Matrices

In this paper we consider a $$2 \times 2$$ operator matrix $$H$$ . We construct an analog of the well-known Faddeev equation for the eigenvectors of $$H$$ and study some important properties of this equation, related with the number of eigenvalues. In particular, the Birman–Schwinger principle for $$H$$ is proven.

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