Abdullaev, Zh. I.; Lakaev, S. N. On the spectral properties of the matrix-valued Friedrichs model. (English) Zbl 0761.47025 Many particle Hamiltonians: spectra and scattering, Adv. Sov. Math. 5, 1-37 (1991). Show indexed articles as search result. [For the entire collection see Zbl 0733.00022.]The authors study the spectral properties of a selfadjoint system \(H\) of integral operators, containing as particular cases some relevant models of mathematical physics. Precisely, \(H\) acts on the Hilbert space \(\mathbb{C}^ n\oplus L_ 2(T^ m,\mathbb{C}^ n)\), where \(T^ m\) is the \(m\)- dimensional torus, and \[ H{f_ 0 \choose f_ 1}={{cf_ 0+\int b(y)f_ 1(y)dy} \choose {b(x)f_ 0+U(x)f_ 1(x)+\int K(x,y)f_ 1(y)dy}}, \] the integration being on \(T^ m\). Applications concern bound states and resonances of the energy operator of a one-magnon-spin-polaron system, resonances of the two-particle cluster operator, bound states and resonances of the discrete two-particle Schrödinger operator. Reviewer: L.Rodino (Torino) Cited in 4 Documents MSC: 47G10 Integral operators 47A40 Scattering theory of linear operators 47A55 Perturbation theory of linear operators Keywords:spectral properties of a selfadjoint system; integral operators; bound states; resonances; energy operator; one-magnon-spin-polaron system; two- particle cluster operator; discrete two-particle Schrödinger operator Citations:Zbl 0733.00022 PDFBibTeX XMLCite \textit{Zh. I. Abdullaev} and \textit{S. N. Lakaev}, in: Many particle Hamiltonians: spectra and scattering, Adv. Sov. Math. 5, . 1--37 (1991; Zbl 0761.47025)