Absolutely continuous spectrum of multidimensional schrödinger operator

International Mathematics Research Notices

Volumn , Issue 74, 2004, Pages 3963-3982

  Denisov, Sergey A ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 13244292400     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s107379280414141x     Document Type: Article

References (24)

1. S. Agmon, Bounds on exponential decay of eigenfunctions of Schrödinger operators, Schrödinger Operators (Como, 1984), Lecture Notes in Mathematics, vol. 1159, Springer, Berlin, 1985, pp. 1-38.
2. _, On the asymptotic behavior of solutions of Schrödinger type equations in unbounded domains, Analyse mathématique et applications, Gauthier-Villars, Montrouge, 1988, pp. 1-22.
3. 2, Discrete Contin. Dyn. Syst. 8 (2002), no. 1, 1-15.
4. _, Random lattice Schrödinger operators with decaying potential: some multidimensional phenomena, Geometric Aspects of Functional Analysis: Israel Seminar 2001-2002 (V. D. Milman and G. Schechtman, Eds.), Lecture Notes in Mathematics, vol. 1807, Springer, Berlin, 2003, pp. 70-98.
5. D. Damanik and R. Killip, Half-line Schrödinger operators with no bound states, to appear in Acta Math.
6. P. Deift and R. Killip, On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials, Comm. Math. Phys. 203 (1999), no. 2, 341-347.
7. S. A. Denisov, On the application of some of M. G. Krein's results to the spectral analysis of Sturm-Liouvitte operators, J. Math. Anal. Appl. 261 (2001), no. 1, 177-191.
8. _, On the existence of the absolutely continuous component for the measure associated with some orthogonal systems, Comm. Math. Phys. 226 (2002), no. 1, 205-220.
9. _, On the absolutely continuous spectrum of Dirac operator, to appear in Comm. Partial Differential Equations.
10. K. Hansson, V. G. Maz'ya, and I. E. Verbitsky, Criteria of solvability for multidimensional Riccati equations, Ark. Mat. 37 (1999), no. 1, 87-120.
11. R. Killip, Perturbations of one-dimensional Schrödinger operators preserving the absolutely continuous spectrum, Int. Math. Res. Not. 2002 (2002), no. 38, 2029-2061.
12. R. Killip and B. Simon, Sum rules for Jacobi matrices and their applications to spectral theory, Ann. of Math. (2) 158 (2003), no. 1, 253-321.
13. A. Kiselev and Y. Last, Solutions, spectrum, and dynamics for Schrödinger operators on infinite domains, Duke Math. J. 102 (2000), no. 1, 125-150.
14. A. Kiselev, Y. Last, and B. Simon, Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators, Comm. Math. Phys. 194 (1998), no. 1, 1-45.
15. M. G. Kreïn, Continuous analogues of propositions on polynomials orthogonal on the unit circle, Dokl. Akad. Nauk SSSR (N.S.) 105 (1955), 637-640.
16. A. Laptev, S. Naboko, and O. Safronov, Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials, to appear in Comm. Math. Phys.
17. _, A Szegö condition for a multidimensional Schrödinger operator, to appear in J. Funct. Anal.
18. V. G. Maz'ya and I. E. Verbitsky, The Schrödinger operator on the energy space: boundedness and compactness criteria, Acta Math. 188 (2002), no. 2, 263-302.
19. S. Molchanov, M. Novitskii, and B. Vainberg, First KdV integrals and absolutely continuous spectrum for 1-D Schrödinger operator, Comm. Math. Phys. 216 (2001), no. 1, 195-213.
20. M. Reed and B. Simon, Methods of Modern Mathematical Physics. III. Scattering Theory, Academic Press, New York, 1979.
21. I. Rodnianski and W. Schlag, Classical and quantum scattering for a class of long range random potentials, Int. Math. Res. Not. 2003 (2003), no. 5, 243-300.
22. O. Safronov, On the absolutely continuous spectrum of multi-dimensional Schrödinger operators with slowly decaying potentials, to appear in Comm. Math. Phys.
23. B. Simon, Schrödinger operators in the twenty-first century, Mathematical Physics 2000, Imperial College Press, London, 2000, pp. 283-288.
24. D. Yafaev, Scattering Theory: Some Old and New Problems, Lecture Notes in Mathematics, vol. 1735, Springer, Berlin, 2000.