Abstract
Using the method of similar operators, we examine spectral properties of the perturbed operator A − B: D(A) ⊂ H → H, where A is a self-adjoint operator with a compact resolvent and B is an unbounded perturbation. Under certain conditions on the spectrum of the unperturbed operator A and the perturbation B, we obtain estimates of the spectral sets of the perturbed operator. The results obtained are applied to the study of the spectrum of differential operators with periodic boundary conditions and a nonsmooth potential.
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