Some spectral properties of periodic potentials

  • V. Guillemin
  • A. Uribe
Chapter
First Online:
Part of the Lecture Notes in Mathematics book series (LNM, volume 1256)

Keywords

Line Bundle Symplectic Form Integral Curve Coset Space Circle Bundle 
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Bibliography

  1. [C]
    P. Cartier, "Quantum mechanical commutation relations and theta functions," Proc. of Symp. in Pure Math. IX, Amer. Math. Soc. Providence, R.I. 361–386 (1966).Google Scholar
  2. [DG]
    J.J. Duistermaat and V. Guillemin, "The spectrum of positive elliptic operators and periodic bicharacteristics," Invent. Math. 29, 39–79 (1975).MathSciNetCrossRefMATHGoogle Scholar
  3. [GS,1]
    V. Guillemin and S. Sternberg, "Some problems in integral geometry and some related problems in micro-local analysis," Am. J. Math. 101, 915–955 (1979).MathSciNetCrossRefMATHGoogle Scholar
  4. [GS,2]
    V. Guillemin and S. Sternberg, "The metaplectic representation, Weyl operators and spectral theory," J. of Funct. Analysis, Vol. 42, 128–225 (1981).MathSciNetCrossRefMATHGoogle Scholar
  5. [GS,3]
    V. Guillemin and S. Sternberg, "A generalization of the notion of polarization" (to appear).Google Scholar
  6. [GU]
    V. Guillemin and A. Uribe, "Clustering theorems with twisted spectra," Math. Ann. 273, 479–506 (1986).MathSciNetCrossRefMATHGoogle Scholar
  7. [LV]
    G. Lion and M. Vergne, The Weil representation, Maslov index and theta series. Progress in Mathematics, Birkhauser, Boston, Basel, Stuttgart (1980).Google Scholar
  8. [U]
    A. Uribe, "Band asymptotics with non-smooth potentials" (to appear).Google Scholar
  9. [W]
    N. Wallach, Symplectic geometry and Fourier analysis. Math. Sci. Press, 53 Jordan Road, Brookline, MA 02146 (1977).MATHGoogle Scholar
  10. [WW]
    E.T. Whittaker and G.N. Watson, A course in modern analysis. Cambridge U. Press, (fourth edition) Cambridge (1927).MATHGoogle Scholar
  11. [ERT]
    G. Eskin, J. Ralston and E. Trubowitz, "On isospectral periodic potentials in ℝn", Comm. P. Appl. Math. 37, 647–676 (1984).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • V. Guillemin
  • A. Uribe

There are no affiliations available

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