The discrete spectrum in the spectral gaps of semibounded operators with non-sign-definite perturbations

Journal of Mathematical Analysis and Applications

Volumn 260, Issue 2, 2001, Pages 641-652

  Safronov, O L ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040376319     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2001.7521     Document Type: Article

References (15)

1. Alama S., Deift P. A., Hempel R. Eigenvalue branches of the Schrödinger operator H - λW in a gap of σ(H). Comm. Math. Phys. 121:1989;291-321.
2. Birman M. Sh. Discrete spectrum in the gaps of a continuous one for perturbations with large coupling constants. Adv. Soviet Math. 7:1991;57-73.
3. Birman M. S., Solomjak M. Z. Spectral Theory of Self-Adjoint Operators in Hilbert Space. Mathematics and Its Applications. 1987;Reidel, Dordrecht.
4. Deift P. A., Hempel R. On the existence of eigenvalues of the Schrödinger operator H - λW in a gap of σ(H). Comm. Math. Phys. 103:1986;461-490.
5. Gesztesy F., Gurarie D., Holden H., Klaus M., Sadun L., Simon B., Vogl P. Trapping and cascading of eigenvalues in the large coupling limit. Comm. Math. Phys. 118:1988;597-634.
6. Gesztesy F., Simon B. On a theorem of Deift and Hempel. Comm. Math. Phys. 116:1988;503-505.
7. Hempel R. On the asymptotic distribution of the eigenvalue branches of a Schrödinger operator H - λW in a spectral gap of H. J. Reine Angew. Math. 399:1989;38-59.
8. Hempel R. Eigenvalues in gaps and decoupling by Neumann boundary conditions. J. Math. Anal. Appl. 169:1992;229-259.
9. Hempel R. On the asymptotic distribution of eigenvalues in gaps. Quasiclassical methods. IMA Vol. Math. Appl. 95:1997;115-124.
10. Klaus M. On the point spectrum of Dirac operators. Helv. Phys. Acta. 53:1980;453-462.
11. Klaus M. Some applications of the Birman-Schwinger principle. Helv. Phys. Acta. 55:1982;49-68.
12. Konno R., Kuroda S. T. On the finiteness of perturbed eigenvalues. J. Fac. Sci. Univ. Tokyo Sect. I. 13:1966;55-63.
13. Levendorskiǐ S. Z. Lower bound for the number of eigenvalue branches for the Schrödinger operator H - λW in a gap of H: The case of indefinite W. Comm. Partial Differential Equations. 20:1995;827-854.
14. Safronov O. L. Discrete spectrum in a gap of the continuous spectrum for variable sign perturbations with large coupling constant. St. Petersburg Math. J. 8:1997.
15. Safronov O. L. The discrete spectrum in the gaps of the continuous one for non-signdefinite perturbations with a large coupling constant. Comm. Math. Phys. 193:1998;233-243.