Geodesic
Main properties of the Faddeev equation for $2 \times 2$ operator matrices
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2023), pp. 53-58

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In the present 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.
Keywords: operator matrix, spectrum, Faddeev equation, operator valued function, Birman–Schwinger principle. 
@article{IVM_2023_12_a3,
     author = {T. H. Rasulov and E. B. Dilmurodov},
     title = {Main properties of the {Faddeev} equation for $2 \times 2$ operator matrices},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {53--58},
     publisher = {mathdoc},
     number = {12},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_12_a3/}
}
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T. H. Rasulov; E. B. Dilmurodov. Main properties of the Faddeev equation for $2 \times 2$ operator matrices. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2023), pp. 53-58. http://geodesic.mathdoc.fr/item/IVM_2023_12_a3/