Absolute continuity of the periodic magnetic Schrödinger operator

Inventiones Mathematicae

Volumn 137, Issue 1, 1999, Pages 85-112

  Sobolev, Alexander V ^a  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

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[No Author keywords available]

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EID: 0033242631     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050324     Document Type: Article

References (17)

1. 1. M. Birman, T. Suslina. Two-dimensional periodic magnetic Hamiltonian is absolutely continuous. Royal Institute of Technology, preprint, September 1996; Algebra i Analiz 9 (1997), no 1, 32-48 (Russian); Engl. transl. in: St Petersburg Math. J. 9 (1998)
2. 1. M. Birman, T. Suslina. Two-dimensional periodic magnetic Hamiltonian is absolutely continuous. Royal Institute of Technology, preprint, September 1996; Algebra i Analiz 9 (1997), no 1, 32-48 (Russian); Engl. transl. in: St Petersburg Math. J. 9 (1998)
3. 1. M. Birman, T. Suslina. Two-dimensional periodic magnetic Hamiltonian is absolutely continuous. Royal Institute of Technology, preprint, September 1996; Algebra i Analiz 9 (1997), no 1, 32-48 (Russian); Engl. transl. in: St Petersburg Math. J. 9 (1998)
4. 2. M. Birman, T. Suslina. Absolute continuity of the two-dimensional periodic magnetic Hamiltonian with discontinuous vector-valued potential. Algebra i Analiz 10 (1998), no 4, 1-36 (Russian); Engl. transl. in: St Petersburg Math. J. 10 (1999), no 4 (to appear)
5. 2. M. Birman, T. Suslina. Absolute continuity of the two-dimensional periodic magnetic Hamiltonian with discontinuous vector-valued potential. Algebra i Analiz 10 (1998), no 4, 1-36 (Russian); Engl. transl. in: St Petersburg Math. J. 10 (1999), no 4 (to appear)
6. n. Theor. Math. Phys. 85 (1990), 1039-1048
7. 4. B.A. Dubrovin, S.P. Novikov. Ground states in a periodic field. Magnetic Bloch functions and vector bundles . Sov. Math. Dokl. 22, 1 (1980), 240-244
8. 5. G. Eskin, J. Ralston. Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy. Commun. Math. Phys. 173 (1995), 199-224
9. 6. R. Hempel, I. Herbst. Strong magnetic fields, Dirichlet boundaries, and spectral gaps. Commun. Math. Phys. 164(1995), 237-259
10. 7. R. Hempel, I. Herbst. Bands and gaps for periodic magnetic Hamiltonians, in Operator Theory: Advances and Applications, vol. 78. Birkhäuser, 1995, 175-184
11. 8. P. Kuchment. Floquet theory for partial differential equations. Birkhäuser, Basel, 1993.
12. 9. T. Kato. Perturbation theory for linear operators. Springer, New York, 1966
13. 10. M. Reed, B. Simon. Methods of modern mathematical physics, IV. Academic Press, New York, 1975
14. 11. Z. Sun. An inverse boundary vaue problem for Schrödinger operators with vector potentials. Trans. AMS 338 (1993), 953-969
15. 12. T. Suslina. Private communication
16. 13. L.E. Thomas. Time dependent approach to scattering from impurities in a crystal. Commun. Math. Phys. 33 (1973), 335-343
17. 14. A. Zygmund. Trigonometric series, II. Cambridge University Press, 1959