Abstract
In this paper, we consider first-order differential operators with periodic boundary conditions acting in a Hilbert space of square summable functions on the segment [0, ω] 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.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 171, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 2, 2019.
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Baskakov, A.G., Krishtal, I.A. & Uskova, N.B. Method of Similar Operators in the Study of Spectral Properties of Perturbed First-Order Differential Operators. J Math Sci 263, 599–615 (2022). https://doi.org/10.1007/s10958-022-05952-3
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DOI: https://doi.org/10.1007/s10958-022-05952-3