We consider the problem of construction of the resolvent of the operator which is a contraction of a given operator to a subspace generated by an orthogonal projection. We establish the equivalence of various methods of construction of these resolvents, and also the connection of this problem with the Vainshtein-Aronshain degenerate-perturbation theory. We show how these problems can be applied to the analysis of spectral properties of the Hamiltonian of a system of several quantum-mechanical particles.
Research Institute of Nuclear Physics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia
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