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This article is cited in 26 scientific papers (total in 26 papers)
On the spectrum of a periodic operator with a small localized perturbation
D. I. Borisov, R. R. Gadyl'shin Bashkir State Pedagogical University
Abstract:
The paper deals with the spectrum of a periodic self-adjoint differential operator on the real axis perturbed by a small localized non-self-adjoint operator. We show that the continuous spectrum does not depend on the perturbation, the residual spectrum is empty, and the point spectrum has no finite accumulation points. We study the problem of the existence of eigenvalues embedded in the continuous spectrum, obtain necessary and sufficient conditions for the existence of eigenvalues, construct asymptotic expansions of the eigenvalues and corresponding eigenfunctions and consider some examples.
Received: 25.08.2006 Revised: 24.03.2008
Citation:
D. I. Borisov, R. R. Gadyl'shin, “On the spectrum of a periodic operator with a small localized perturbation”, Izv. RAN. Ser. Mat., 72:4 (2008), 37–66; Izv. Math., 72:4 (2008), 659–688
Linking options:
https://www.mathnet.ru/eng/im1146https://doi.org/10.1070/IM2008v072n04ABEH002420 https://www.mathnet.ru/eng/im/v72/i4/p37
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