Abstract
Let A be a self-adjoint operator, let (α,β) be a gap in the spectrum of A, and let B=A+V, where, in general, the perturbation operator V is unbounded. We establish some abstract conditions under which the spectrum of B in (α,β) is discrete; does not accumulate to β; is finite. An estimate of the number of eigenvalues of B in (α,β) is obtained. Bibliography: 3 titles.
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References
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Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 237–241.
Translated by S. V. Kislyakov.
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Sloushch, V.A. Discrete spectrum in spectral gaps of a self-adjoint operator under unbounded perturbations. J Math Sci 101, 3190–3192 (2000). https://doi.org/10.1007/BF02673743
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DOI: https://doi.org/10.1007/BF02673743