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).

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[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)


47G10 Integral operators
47A40 Scattering theory of linear operators
47A55 Perturbation theory of linear operators


Zbl 0733.00022