T. H. Rasulov, E. B. Dilmurodov, “Main properties of the Faddeev equation for <nobr>$2 \times 2$</nobr> operator matrices”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, Number 12,Pages <nobr>53

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

T. H. Rasulov^a, E. B. Dilmurodov^ba

^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

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.

UDC: 517.984

Received: 29.03.2023
Revised: 07.05.2023
Accepted: 29.05.2023

DOI: 10.26907/0021-3446-2023-12-53-58