Geodesic
Method of similar operators in the study of spectral properties of perturbed first-order differential 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. 3-18

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In this paper, we considers first-order differential operators with periodic boundary conditions acting in a Hilbert space of square summable functions on the segment $[0,\omega] $ perturbed by Hilbert–Schmidt integral operators. A similarity transformation of the original operator to the operator of the block-diagonal structure is performed; this allows one to study spectral properties of the perturbed operator. The research method is the method of similar operators, which also presented in this work.
Keywords: method of similar operators, spectrum, integro-differential operator. 
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     author = {A. G. Baskakov and I. A. Krishtal and N. B. Uskova},
     title = {Method of similar operators in the study of spectral properties of perturbed first-order differential operators},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--18},
     publisher = {mathdoc},
     volume = {171},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_171_a0/}
}
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A. G. Baskakov; I. A. Krishtal; N. B. Uskova. Method of similar operators in the study of spectral properties of perturbed first-order differential 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. 3-18. http://geodesic.mathdoc.fr/item/INTO_2019_171_a0/