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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, Number 12, Pages 53–58
DOI: https://doi.org/10.26907/0021-3446-2023-12-53-58 (Mi ivm9925) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Main properties of the Faddeev equation for $2 \times 2$ operator matrices

T. H. Rasulova, E. B. Dilmurodovba

a Bukhara State University, 11 M. Ikbol str., Bukhara, 200118 Uzbekistan
b Bukhara Branch of the Institute of Mathematics named after V.I.Romanovskiy of the Academy of Sciences of the Republic of Uzbekistan, 11 M. Ikbol str., Bukhara, 200118 Uzbekistan
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DOI: https://doi.org/10.26907/0021-3446-2023-12-53-58
Abstract: 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.
Received: 29.03.2023
Revised: 07.05.2023
Accepted: 29.05.2023
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2023, Volume 67, Issue 12, Pages 47–52
DOI: https://doi.org/10.3103/S1066369X2312006X
Document Type: Article
UDC: 517.984
Language: Russian
Citation: T. H. Rasulov, E. B. Dilmurodov, “Main properties of the Faddeev equation for $2 \times 2$ operator matrices”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 12, 53–58; Russian Math. (Iz. VUZ), 67:12 (2023), 47–52
Citation in format AMSBIB
\Bibitem{RasDil23}
\by T.~H.~Rasulov, E.~B.~Dilmurodov
\paper Main properties of the Faddeev equation for $2 \times 2$ operator matrices
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 12
\pages 53--58
\mathnet{http://mi.mathnet.ru/ivm9925}
\crossref{https://doi.org/10.26907/0021-3446-2023-12-53-58}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2023
\vol 67
\issue 12
\pages 47--52
\crossref{https://doi.org/10.3103/S1066369X2312006X}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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