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Zapiski Nauchnykh Seminarov POMI, 1997, Volume 247, Pages 237–241 (Mi znsl573)  

Discrete spectrum in the spectral gaps of a selfadjoint operator for unbounded perturbations

V. A. Sloushch

Saint-Petersburg State University
Abstract: 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.
Received: 15.03.1997
English version:
Journal of Mathematical Sciences (New York), 2000, Volume 101, Issue 3, Pages 3190–3192
DOI: https://doi.org/10.1007/BF02673743
Bibliographic databases:
UDC: 517.43
Language: Russian
Citation: V. A. Sloushch, “Discrete spectrum in the spectral gaps of a selfadjoint operator for unbounded perturbations”, Investigations on linear operators and function theory. Part 25, Zap. Nauchn. Sem. POMI, 247, POMI, St. Petersburg, 1997, 237–241; J. Math. Sci. (New York), 101:3 (2000), 3190–3192
Citation in format AMSBIB
\Bibitem{Slo97}
\by V.~A.~Sloushch
\paper Discrete spectrum in the spectral gaps of a~selfadjoint operator for unbounded perturbations
\inbook Investigations on linear operators and function theory. Part~25
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 247
\pages 237--241
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl573}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1692675}
\zmath{https://zbmath.org/?q=an:0964.47003}
\transl
\jour J. Math. Sci. (New York)
\yr 2000
\vol 101
\issue 3
\pages 3190--3192
\crossref{https://doi.org/10.1007/BF02673743}
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