Inverse problem for the discrete 1D Schrödinger operator with small periodic potentials

Communications in Mathematical Physics

Volumn 261, Issue 3, 2006, Pages 673-692

  Korotyaev, Evgeny ^a   Kutsenko, Anton ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29144461963     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-005-1429-z     Document Type: Article

References (20)

1. [AS] Abramowitz, M., Stegun, I.A.: Handbook of mathematical functions with formulas, graphs, and mathematical tables. Washington, D.C.: U.S. Government Printing Office, 1964
2. [BGGK] Bättig, D., Grebert, B., Guillot, J.-C., Kappeler, T.: Fibration of the phase space of the periodic Toda lattice. J. Math. Pures Appl. (9) 72, no. 6, 553-565 (1993)
3. [GT] Garnett J., Trubowitz E.: Gaps and bands of one dimensional periodic Schrödinger operators. Comment. Math. Helv. 59, 258-312 (1984)
4. [GKT] Gieseker, D., Knörrer, H., Trubowitz, E.: The geometry of algebraic Fermi curves. Perspectives in Mathematics 14, Boston, MA: Academic Press, Inc., 1993
5. [KK] Kargaev, P., Korotyaev, E.: Inverse Problem for the Hill Operator, the Direct Approach. Invent. Math. 129, no. 3, 567-593 (1997)
6. [K1] Korotyaev, E.: The inverse problem for the Hill operator. I. Internat. Math. Res. Notices 3, 113-125 (1997)
7. [K2] Korotyaev, E.: The inverse problem and trace formula for the Hill operator, U. Math. Z. 231, 345-368 (1999)
8. [K3] Korotyaev, E.: Characterization of the spectrum of Schrödinger operators with periodic distributions, Int. Math. Res. Not. 37, 2019-2031 (2003)
9. [K4] Korotyaev, E.: Gap-length mapping for periodic Jacobi matrices. Preprint 2004
10. [KKr] Korotyaev, E., Krasovsky, I.: Spectral estimates for periodic Jacobi matrices. Comm. Math. Phys. 234, no. 3, 517-532 (2003)
11. [KKu1] Korotyaev, E., Kutsenko, A.: Inverse problem for the periodic Jacoby matrices. Preprint 2004
12. [KKu2] Korotyaev, E., Kutsenko, A.: Inverse problem for the discrete ID Schrödinger operator with large periodic potential. Preprint 2004
13. [L] Last, Y.: On the measure of gaps and spectra for discrete ID Schrodinger operators. Comm. Math. Phys. 149, no. 2, 347-360 (1992)
14. [M] Marchenko, V.: Sturm-Liouvill operator and applications. Basel: Birkhauser 1986
15. [MO1] Marchenko, V., Ostrovski, I.: A characterization of the spectrum of the Hill operator. Math. USSR Sbornik 26, 493-554 (1975)
16. [MO2] Marchenko, V., Ostrovski, I.: Approximation of periodic by finite-zone potentials. Selecta Math. Sovietica. 6, No 2, 101-136 (1987)
17. [Pe] Perkolab, L.: An inverse problem for a periodic Jacobi matrix. (Russian) Teor. Funktsii Funktsional. Anal. i Prilozhen. 42, 107-121 (1984)
18. [Te] Teschl, G.: Jacobi operators and completely integrable nonlinear lattices. Mathematical Surveys and Monographs, 72. Providence, RI: American Mathematical Society, 2000
19. [vM] van Moerbeke, P.: The spectrum of Jacobi matrices. Invent. Math. 37, no. 1, 45-81 (1976)
20. [vMou] van Mouche, P.: Spectral asymptotics of periodic discrete Schrodinger operators. I. Asymptotic Anal. 11, no. 3, 263-287 (1995)