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Acta Mathematica

, Volume 179, Issue 2, pp 153–196 | Cite as

Discrete one-dimensional quasi-periodic Schrödinger operators with pure point spectrum

  • L. H. Eliasson
Article

Keywords

Point Spectrum Pure Point Pure Point Spectrum 
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References

  1. [1]
    Carmona, R. &Lacroix, J.,Spectral Theory of Random Schrödinger Operators, Birkhäuser, Boston, MA, 1990.Google Scholar
  2. [2]
    Chulaevsky, V. A. &Dinaburg, E. I. Methods of KAM-theory for long-range quasiperiodic operators onZ v. Pure point spectrum.Comm. Math. Phys. 153 (1993), 559–577.CrossRefMathSciNetGoogle Scholar
  3. [3]
    Coddington, E. A. &Levinson, N.,Theory of Ordinary Differential Equations, McGraw-Hill, New York-Toronto-London, 1955.Google Scholar
  4. [4]
    Eliasson, L. H., Floquet solutions for the one-dimensional quasi-periodic Schrödinger equation.Comm. Math. Phys., 146 (1992), 447–482.CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    Folland, G. D.,Introduction to Partial Differential Equations. Princeton Univ. Press, Princeton, NJ, 1976.Google Scholar
  6. [6]
    Friedrichs, K. O.,Perturbation of Spectra in Hilbert Space. Amer. Math. Soc., Providence, RI, 1965.Google Scholar
  7. [7]
    Fröhlich, J., Spencer, T. &Wittver, P., Localization for a class of one-dimensional quasi-periodic Schrödinger operators.Comm. Math. Phys., 132 (1990), 5–25.CrossRefMathSciNetGoogle Scholar
  8. [8]
    Jitomirskaya, S. Ya., Anderson localization for the almost Matheiu, equation: a nonperturbative proof.Comm. Math. Phys., 165 (1994), 49–57.CrossRefzbMATHMathSciNetGoogle Scholar
  9. [9]
    Jitomirskaya, S. &Simon, B., Operators with singular continuous spectrum, III: almost periodic Schrödinger operators.Comm. Math. Phys., 165 (1994), 201–205.CrossRefMathSciNetGoogle Scholar
  10. [10]
    Kato, T.,Perturbation Theory of Linear Operators. Second edition. Springer-Verlag, Berlin-New York, 1976.Google Scholar
  11. [11]
    MacDonald, I. G.,Symmetric Functions and Hall Polynomials. Clarendon Press, Oxford, 1979.Google Scholar
  12. [12]
    Pyartli, A. S., Diophantine approximation on submanifolds of Euclidean space.Functional Anal. Appl., 3 (1969), 303–306.CrossRefzbMATHGoogle Scholar
  13. [13]
    Rudin, W.,Real and Complex Analysis. McGraw-Hill, New York-Toronto-London, 1966.Google Scholar
  14. [14]
    Sinai, Ya. G., Anderson localization for the one-dimensional difference Schrödinger operator with a quasi-periodic potential.J. Statist. Phys., 46 (1987), 861–909.CrossRefMathSciNetGoogle Scholar

Copyright information

© Institut Mittag-Leffler 1997

Authors and Affiliations

  • L. H. Eliasson
    • 1
  1. 1.Department of MathematicsRoyal Institute of TechnologyStockholmSweden

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