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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. 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.

UDC: 517.43

Received: 15.03.1997


 English version:
Journal of Mathematical Sciences (New York), 2000, 101:3, 3190–3192

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