The Discrete Spectrum in the Spectral Gaps of Semibounded Operators with Non-sign-definite Perturbations
✍ Scribed by O.L. Safronov
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 105 KB
- Volume
- 260
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
Given two self-adjoint operators A and V = V + -V -, we study the motion of the eigenvalues of the operator A t = A -tV as t increases. Let α > 0 and let λ be a regular point for A. We consider the quantities N + V λ α , N -V λ α , and N 0 V λ α defined as the number of eigenvalues of the operator A t that pass point λ from the right to the left, from the left to the right, or change the direction of their motion exactly at point λ, respectively, as t increases from 0 to α > 0. We study asymptotic characteristics of these quantities as α → ∞. In the present paper, the results obtained previously [O. L. Safronov, Comm. Math. Phys. 193 (1998), 233-243] are extended and given new applications to differential operators.