Eigenvalue asymptotics for the schrödinger operator with homogeneous magnetic potential and decreasing electric potential. i. behaviour near the essential spectrum tips

Communications in Partial Differential Equations

Volumn 15, Issue 3, 1990, Pages 407-434

  Raikov, George D ^a  

^a INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84972899563     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605309908820690     Document Type: Article

References (19)

1. J. Avron, I. Herbst, B. Simon. Schrodinger operators with magnetic fields. I. General interactions. Duke. Math. J. 45 (1978) 847—883.
2. F.A.Berezin, M.A.Shubin. Schrodinger's equation. Izdat. Moskovsk. Univ., Moscow, 1983 (Russian
3. M.S. Birman M.Z., Solomjak. Estimates for the singular numbers of integral operators. Uspehi Mat Nauk 32 C19771 17-84; English transl. in Russian Math Surveys 32 (1977
4. M.S.Birman, M.Z.Solomjak. Quantitative analysis in Sobolev imbedding theorems and applications to spectral theory. AMS Translations, Series 2, 114 AMS, Providence, R.I, 1980
5. M.S.Birman, M.Z.Solomjak. Spectral Theory of Selfadjoint Operators in Hilbert Space. Dodrecht, Holland, D. Reidel Publishing Company, 1987.
6. Y.Colin de Verdire. L’asymptotique de Weyl pour les bouteilles magnetiques, Commun. Math. Phys. 105 (1986) 327–335
7. M. Dauge, D. Robert. Weyl's formula for a class of pseudodifferential operators of negative order on L2(Rn), Journees de Saint Jean de Monts (1986) 92–122
8. B. Helffer, A. Mohamed. Caracterisation du spectre essentiel de l'opérateur de Schrodinger avec un champ magnétique. Ann. Inst. Fourier 38, 2 (1988) 95–112
9. L.Hormander. The Weyl calculus of pseudodifferential operators. Commun. Pure Appl. Math. 32 (1979) 359–443
10. V.Ya. Ivrii. Bounds for the number of negative eigenvalues of the Schrodinger operator with a strong magnetic field. Soviet Math. Dokl. 36 (1988) 561-564
11. V.Ya. Ivrii. Sharp spectral asymptotics for the two-dimensional Schrodinger operators with a strong magnetic field. Dokl. Akad. Nauk SSSR 306 (1989) 31–34 (Russian
12. H.Leinfelder, C.G.Simader. Schrodinger operators with singular magnetic vector potentials. Math. Z. 176 (1981) 1–19
13. (13] G.D.Raikov. Eigenvalue asymptotics for the Schrodinger operator with homogeneous magnetic potential and decreasing electric potential. I. Behaviour near the essential spectrum tips. C. R. Acad. Sci. Paris 309 (1989) 559-564
14. G.V.Rozenbljum. An asymptotic of the negative discrete spectrum of the Schrodinger operator. Math. Notes USSR 21 (1977) 222–227
15. M.A.Shubin. Fseudodiffevential Operators and Spectral Theory. Nauka, Moscow, 1978 (Russian
16. A.V.Sobolev. Asymptotic behaviour of the energy levels of a quantum particle in a homogeneous magnetic field perturbed by a decreasing electric field, I. J. Sov. Math. 35 (1986) 2201–2211
17. S.N.Solnyshkin. Asymptotics of the energy of bound states of the Schrodinger operator in the presence of electric and homogeneous magnetic fields. Selecta Math. Soviet. 5 (1986) 297–306.
18. H. Tamura. Asymptotic distribution of eigenvalues for Schrodinger operators with magnetic fields. Nagoya Math. J. 105 (1987) 49–69
19. H.Tamura. Asymptotic distribution or eigenvalues for Schrodinger operators with homogeneous magnetic fields. Osaka J. Math. 23 (1988) 633–647.