Bounds on embedded singular spectrum for one-dimensional schrödinger operators

Proceedings of the American Mathematical Society

Volumn 128, Issue 1, 2000, Pages 161-171

  Remling, Christian ^a  

^a UNIVERSITY OF OSNABRÜCK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22844454912     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-99-05110-2     Document Type: Article

References (20)

1. M. Christ and A. Kiselev, Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results, to appear in J. Amer. Math. Soc. CMP 98:12
2. M. Christ, A. Kiselev, and C. Remling, The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials, Math. Research Letters 4 (1997), 719-723. CMP 98:05
3. R. del Rio, S. Jitomirskaya, Y. Last, and B. Simon, Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization, J. d'Analyse Math. 69 (1996), 153-200. MR 97m:47002
4. F. Delyon, B. Simon, and B. Souillard, From power pure point to continuous spectrum in disordered systems, Ann. Inst. H. Poincaré 42 (1985), 283-309. MR 87d:35098
5. M.S.P. Eastham, The Asymptotic Solution of Linear Differential Systems, London Math. Soc. Monographs New Series 4, Clarendon Press, Oxford, 1989. MR 91d:34001
6. K.J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, Cambridge, 1985. MR 88d:28001
7. A. Kiselev, Preservation of the absolutely continuous spectrum of Schrödinger equations under perturbations by slowly decreasing potentials and a.e. convergence of integral operators, Duke Math. J. 94 (1998), 619-646. CMP 98:17
8. A. Kiselev, Interpolation theorem related to a.e. convergence of integral operators, to appear in Proc. Amer. Math. Soc.
9. Y. Last, Quantum dynamics and decompositions of singular continuous spectra, J. Funct. Anal. 142 (1996), 406-445. MR 97k:81044
10. S.N. Naboko, Dense point spectra of Schrödinger and Dime operators, Theor. and Math. Phys. 68 (1986), 646-653. MR 88h:81029
11. M. Reed and B. Simon, Methods of Modern Mathematical Physics, III. Scattering Theory, Academic Press, London-San Diego, 1979. MR 80m:81085
12. C. Remling, The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials, Commun. Math. Phys. 193 (1998), 151-170. CMP 98:11
13. C. Remling, Embedded singular continuous spectrum for one-dimensional Schrödinger operators, to appear in Trans. Amer. Math. Soc.
14. B. Simon, Some Jacobi matrices with decaying potentials and dense point spectrum, Commun. Math. Phys. 87 (1982), 253-258. MR 85d:47033
15. B. Simon, Some Schrödinger operators with dense point spectrum, Proc. Amer. Math. Soc. 125 (1997), 203-208. MR 97c:34179
16. G. Stolz, Bounded solutions and absolute continuity of Sturm-Liouville operators, 3. Math. Anal. Appl. 169 (1992), 210-228. MR 93f:34141
17. R. Strichartz, Fourier asymptotics of fractal measures, J. Funct. Anal. 89 (1990), 154-187. MR 91m:42015
18. J. von Neumann and E. Wigner, Über merkwürdige diskrete Eigenwerte, Z. Phys. 30 (1929), 465-467.
19. J. Weidmann, Spectral Theory of Ordinary Differential Operators, Springer Lect. Notes 1258, Springer-Verlag, Berlin, 1987. MR 89b:47070
20. A. Zygmund, Trigonometric Series, vol. I, II, Cambridge University Press, Cambridge, 1959. MR 21:6498