Keywords
- Line Bundle
- Symplectic Form
- Integral Curve
- Coset Space
- Circle Bundle
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Bibliography
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).
J.J. Duistermaat and V. Guillemin, "The spectrum of positive elliptic operators and periodic bicharacteristics," Invent. Math. 29, 39–79 (1975).
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).
V. Guillemin and S. Sternberg, "The metaplectic representation, Weyl operators and spectral theory," J. of Funct. Analysis, Vol. 42, 128–225 (1981).
V. Guillemin and S. Sternberg, "A generalization of the notion of polarization" (to appear).
V. Guillemin and A. Uribe, "Clustering theorems with twisted spectra," Math. Ann. 273, 479–506 (1986).
G. Lion and M. Vergne, The Weil representation, Maslov index and theta series. Progress in Mathematics, Birkhauser, Boston, Basel, Stuttgart (1980).
A. Uribe, "Band asymptotics with non-smooth potentials" (to appear).
N. Wallach, Symplectic geometry and Fourier analysis. Math. Sci. Press, 53 Jordan Road, Brookline, MA 02146 (1977).
E.T. Whittaker and G.N. Watson, A course in modern analysis. Cambridge U. Press, (fourth edition) Cambridge (1927).
G. Eskin, J. Ralston and E. Trubowitz, "On isospectral periodic potentials in ℝn", Comm. P. Appl. Math. 37, 647–676 (1984).
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© 1987 Springer-Verlag
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Guillemin, V., Uribe, A. (1987). Some spectral properties of periodic potentials. In: Cordes, H.O., Gramsch, B., Widom, H. (eds) Pseudo-Differential Operators. Lecture Notes in Mathematics, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077744
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DOI: https://doi.org/10.1007/BFb0077744
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