This article is cited in 6 papers

On the existence of an eigenvalue of the generalized Friedrichs model

M. I. Muminov, U. R. Shadiev

Samarkand State University, 15 University blvd., Samarkand, 140104 Republic of Uzbekistan

Abstract: We consider a family of bounded self-adjoint matrix operators (generalized Friedrichs models) acting on the direct sum of one-particle and two-particle subspaces of the Fock space. Conditions for the existence of eigenvalues of the matrix operators are obtained.

Keywords: Friedrichs model, subspace of the Fock space, eigenvalue, essential spectrum.

UDC: 517.984

Received: 11.02.2023
Revised: 25.03.2023
Accepted: 29.03.2023

DOI: 10.26907/0021-3446-2024-4-31-38

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2024, 68:4, 28–34