On the number of negative eigenvalues for a Schrödinger operator with magnetic field

Communications in Mathematical Physics

Volumn 182, Issue 3, 1996, Pages 637-660

  Shen, Zhongwei ^a  

^a UNIVERSITY OF KENTUCKY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030569491     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02506420     Document Type: Article

References (19)

1. Avron, J., Herbst, I., Simon, B.: Schrödinger Operators with Magnetic Fields. I. General Interaction. Duke Math. J. 45(4), 847-883 (1978)
2. P Estimates for Fractional Integrals and Sobolev Inequalities with Applications to Schrödinger Operators. Comm. in P. D. E. 10, 1077-1116 (1985)
3. Fefferman, C.: The Uncertainty Principle. Bull. Am. Math. Soc. 9, 129-206 (1983)
4. Helffer, B.: Semi-Classical Analysis for the Schrödinger Operator and Applications. Lecture Notes in Math. 1336, Berlin-Heidelberg-New York: Springer Verlag, 1988
5. Helfer, B., Nourrigat, J.: Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs. Progress in Math. 58, Boston: Birkhäuser, 1985
6. Iwatsuka, A.: Magnetic Schrödinger Operators with Compact Resolvent. J. Math. Kyoto Univ. 26(3), 357-374 (1986)
7. Kerman, R., Sawyer, E.: The Trace Inequality and Eigenvalue Estimates for Schrödinger Operators. Ann. Inst. Fourier(Grenoble) 36(4), 207-228 (1986)
8. Leinfelder, H., Simader, C.: Schrödinger Operators with Singular Magnetic Vector Potentials. Math. Z. 176, 1-19 (1981)
9. Mohamed, A., Raikov, G.: On the Spectral Theory of the Schrödinger Operator with Electronmagnetic Potential. In: Pseudo-Differential Calculus and Mathematical Physics, edited by M. Demuth, E. Schrohe and B.W. Schulze, Berlin: Akademie Verlag, 1994, pp. 298-390
10. Robert, D.: Comportement asymptotique des valurs propres d'opérateurs du type Schrödinger à potentiel "dégénéré". J. Math. Pures Appl. 61(9), 275-300 (1982)
11. P Estimates for Schrödinger Operators with Certain Potentials. Ann. Inst. Fourier (Grenoble) 45(2), 513-546 (1995)
12. Shen, Z.: On the Eigenvalue Asymptotics of Schrödinger Operators. Preprint (1995)
13. Shen, Z.: Eigenvalue Asymptotics and Exponential Decay of Eigenfunctions for Schrödinger Operators with Magnetic Fields. Trans. Am. Math. Soc. (to appear)
14. P for Magnetic Schrödinger Operators. Preprint (1995)
15. Simon, B.: Schrödinger Semigroups. Bull. Am. Math. Soc. 7(3), 447-525 (1982)
16. Simon, B.: Functional Integration and Quantum Physics. New York: Academic Press, 1979
17. Simon, B.: Nonclassical Eigenvalue Asymptotics. J. Funct. Anal. 53, 84-98 (1983)
18. Stein, E.: Singular Integrals and Diffentiability Properties of Functions. Princeton, NJ: Princeton Univ. Press, 1970
19. Stein, E.: Harmonic Analysis: Real-Variable Method, Orthogonality, and Oscillatory Integrals. Princeton, NJ: Princeton Univ. Press, 1993