Geodesic
Discrete spectrum in the spectral gaps of a selfadjoint operator for unbounded perturbations
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 25, Tome 247 (1997), pp. 237-241 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $A$ be a selfadjoint operator, $(\alpha,\beta)$ a gap in the spectrum of $A$, $B=A+V$, where, in general, the perturbation operator $V$ is unbounded. We establish some abstract conditions under which the spectrum of $B$ on $(\alpha,\beta)$ is discrete; does not accumulate to $\beta$; is finite. An estimate of the number of the eigenvalues of $B$ on $(\alpha,\beta)$ is obtained. 
@article{ZNSL_1997_247_a14,
     author = {V. A. Sloushch},
     title = {Discrete spectrum in the spectral gaps of a~selfadjoint operator for unbounded perturbations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {237--241},
     year = {1997},
     volume = {247},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_247_a14/}
}
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V. A. Sloushch. Discrete spectrum in the spectral gaps of a selfadjoint operator for unbounded perturbations. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 25, Tome 247 (1997), pp. 237-241. http://geodesic.mathdoc.fr/item/ZNSL_1997_247_a14/