Absolutely continuous spectrum of perturbed stark operators

Transactions of the American Mathematical Society

Volumn 352, Issue 1, 2000, Pages 243-256

  Kiselev, Alexander ^a,b  

^a MATHEMATICAL SCIENCES RESEARCH INSTITUTE   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22844453651     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02450-2     Document Type: Article

References (22)

1. 3. Ascii, P. Duclos and P. Exncr, Stark- Wannier Hamiltonians with pure point spectrum, in Differential Equations, Asymptotic Analysis, and Mathematical Physics (Potsdam, 1996), Akademie Vorlag, Berlin, 1997.MR98f: 810G6
2. 3. Avron and B. Simon, Transient and recurrent spectrum, 3. Funct. Anal. 43(1981), 1-31.MR 83c: 47008
3. 3.E. Avron, P. Exner and Y. Last, Periodic Schrodinger operators with large gaps and Wannier-Stark ladders, Phys. Rev. Lett. 72(1994), 89G-899.
4. F. Bentosela et al., Schrodinger operators with an electric field and random or deterministic potentials, Commun. Math. Phys. 88(1983), 387-397.MR 85f: 34036
5. P. Exner, The absence of the absolutely continuous spectrum for 6' Wannier-Stark ladders, 3. Math. Phys. 36(9) (1995), 4561-1570.MR 96g: 81050
6. D.3. Gilbert, On subordinacy and analysis of the spectrum of Schrodinger operators with two singular endpoints, Proc. Roy. Soc. Edinburgh Sect. A 112(1989), 213-229.MR 90j: 47061
7. D.3. Gilbert and D.B. Pearson, On subordinacy and analysis of the spectrum of one-dimensional Schrodinger operators, 3. Math. Anal. Appl. 128(1987), 30-56.MR 89a: 34033
8. P. Hartman, Ordinary Differential Equations, Birkhäuser, Boston 1982.MR 83e: 34002
9. A. Kiselev, Absolutely continuous spectrum of one-dimensional Schrodinger operators and Jacobi matrices with slowly decaying potentials, Commun. Math. Phys.l79(1996), 377-400.MR 97o: 81027
10. A. Kiselev, Stability of the absolutely continuous spectrum of Schrodinger equation under perturbations by slowly decreasing potentials and o.e. convergence of integral operators, Duke Math. J. 94(1998), 619-646. CMP 98: 17
11. A. Kiselev and B. Simon, Rank one perturbations in infinitesmal coupling, 3. Funct. Anal. 130(1)(1995), 345-356.MR 96e: 47012
12. Y. Last, Quantum dynamics and decompositions of singular continuous spectra, 3. Funct. Anal. 142(2)(1996), 406-445.MR 97k: 81044
13. S.N. Naboko, Dense point spectra of Dirac and Schrodinger operators, Thoor. Math. 68(1986), 18-28.MR 88h: 81029
14. S.N. Naboko and A.B. Pushnitsldi, Point spectrum on a continuous spectrum for weakly perturbed Stark type operators, Funct. Anal. Appl. 29(4)(1995), 248-257.MR 96k: 34187
15. 3. von Neumann and E.P. Wigner, Ober merkwürdige diskrete eigenwerte, Z. Phys. 30(1929), 465-467.
16. W. Rudin, Real and Complex Analysis, New York, McGraw-Hill, 1987.MR 88k: 00002
17. 3. Sahbani, Propagation theorems for some classes of pseudodifferential operators, 3. Math. Anal. Appl. 211 (1997), 481-497.MR 98e: 47078
18. B. Simon, Spectral analysis of rank one perturbations and applications, Proc. 1993 Vancouver Summer School in Mathematical Physics.
19. B. Simon, Bounded eigenfunctions and absolutely continuous specta for one-dimensional Schrodinger operators, Proc. Amer. Math. Soc. 124(11), 3361-3369.MR 97a: 34223
20. G. Stolz, Bounded solutions and absolute continuity of Sturm-Liouville operators, 3. Math. Anal. Appl. 169(1992), 210-228.MR 93f: 34141
21. 3. Walter, Absolute continuity of the essential spectrum of-d/dx2+q(x) without monotony 0/9, Math. Z. 129(1)(1972), 83-94.MR 48: 4399
22. A. Zygmund, A remark on Fourier transforms, Proc. Camb. Phil. Soc. 32, 321-327 (1936).