Skip to main content
Log in

On the spectrum of lattice Schrödinger operators with deterministic potential

  • Published:
Journal d'Analyse Mathématique Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. J. Bourgain,Positive Lyapounov exponents for most energies, inGeometric Aspects of Functional Analysis, Lecture Notes in Math.1745, Springer, Berlin, 2000, pp. 37–66.

    Chapter  Google Scholar 

  2. J. Bourgain,Estimates on Green’s functions, Localization and the quantum kicked rotor model, Ann. of Math. (2) (2002), to appear.

  3. J. Bourgain and M. Goldstein,On nonperturbative localization with quasi-periodic potential, Ann. of Math. (2)152 (2000), 835–879.

    Article  MathSciNet  Google Scholar 

  4. J. Bourgain, M. Goldstein and W. Schlag,Anderson localization for Schrödinger operators on Z with potentials given by the skew-shift, Comm. Math. Phys. to appear.

  5. M. Goldstein and W. Schlag,Hölder continuity of the integrated density of states for quasiperiodic Schrödinger equations and averages of shifts of subharmonic functions, Ann. of Math. (2)154 (2001), 155–203.

    Article  MathSciNet  Google Scholar 

  6. S. Jitomirskaya,Metal-insulator transition for the almost Mathieu operator, Ann. of Math. (2)150 (1999), 1159–1175.

    Article  MathSciNet  Google Scholar 

  7. Y. Last,Almost everything about the almost Mathieu operator I, inProc. XI Internat. Congr. Math. Phys. (Paris 1994), Internat. Press, Cambridge, MA, 1995, pp. 366–372.

    Google Scholar 

  8. J. Milnor,On the Betti numbers of real varieties, Proc. Amer. Math. Soc.15 (1964), 275–280.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Bourgain.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bourgain, J. On the spectrum of lattice Schrödinger operators with deterministic potential. J. Anal. Math. 87, 37–75 (2002). https://doi.org/10.1007/BF02868469

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02868469

Navigation