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On Spectral Properties of a Certain Class of Perturbed Operators

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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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Authors and Affiliations

  1. Voronezh State Pedagogical University, Voronezh, Russia

    G. V. Garkavenko

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  1. G. V. Garkavenko
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Correspondence to G. V. Garkavenko.

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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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Garkavenko, G.V. On Spectral Properties of a Certain Class of Perturbed Operators. J Math Sci 263, 653–665 (2022). https://doi.org/10.1007/s10958-022-05956-z

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  • DOI: https://doi.org/10.1007/s10958-022-05956-z

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