Spectrum and resolvent of the friedrichs model with rank 3 perturbation

Аннотация

In this article, we consider a bounded and self-adjoint Friedrichs model 𝐴 with rank 3 perturbation. This model is associated to a system of two particles on the 𝑑-dimensional lattice 𝑍𝑑. The number and location of the discrete eigenvalues of the model 𝐴 are studied. Conditions for the existence of these eigenvalues are found and their multiplicity is determined. Corresponding eigenfunctions are found. An explicit form of the resolvent of the model 𝐴 is constructed.