Geodesic
On spectral properties of a certain class of perturbed operators
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 57-69

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Using the method of similar operators, we examine spectral properties of the perturbed operator ${A-B}:D(A)\subset H \to H$, 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.
Keywords: method of similar operators, spectrum, differential operator. 
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     author = {G. V. Garkavenko},
     title = {On spectral properties of a certain class of perturbed operators},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {57--69},
     publisher = {mathdoc},
     volume = {171},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_171_a4/}
}
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G. V. Garkavenko. On spectral properties of a certain class of perturbed operators. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 57-69. http://geodesic.mathdoc.fr/item/INTO_2019_171_a4/