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Clustering theorems with twisted spectra

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References

  1. Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-duality in four-dimensional Riemannian geometry. Proc. R. Soc. Lond. A362, 425–461 (1978)

    Google Scholar 

  2. Boutet de Monvel, L., Guillemin, V.: The spectral theory of Toeplitz operators. Annals of Mathematics Studies No. 99. Princeton: Princeton University Press 1981

    Google Scholar 

  3. Colin de Verdiére, Y.: Sur le spectre des operateurs elliptiques à bicaracteristiques toutes périodiques. Comment. Math. Helv.54, 508–522 (1979)

    Google Scholar 

  4. Duistermaat, J.J., Guillemin, V.: The spectrum of positive elliptic operators and periodic bicharacteristics. Invent. Math.29, 39–79 (1975)

    Google Scholar 

  5. Eskin, G., Ralston, J., Trubowitz, E.: On isospectral periodic potentials in 506-1. Commun. Pure Appl. Math.37, 647–676. II: 715–753 (1984)

    Google Scholar 

  6. Guillemin, V.: Spectral theory onS 2: some open questions. Adv. Math.42, 283–298 (1981)

    Google Scholar 

  7. Guillemin, V.: Band asymptotics in two dimensions. Adv. Math.42, 248–282 (1981)

    Google Scholar 

  8. Guillemin, V., Sternberg, S.: Homogeneous quantization and multiplicities of group representations. J. Funct. Anal.47, 344–380 (1982)

    Google Scholar 

  9. Guillemin, V., Sternberg, S.: Symplectic techniques in physics. Cambridge: Cambridge University Press 1984

    Google Scholar 

  10. Guillemin, V., Sternberg, S.: Some problems in integral geometry and some related problems in micro-local analysis. Am. J. Math.101, 915–955 (1979)

    Google Scholar 

  11. Helgason, S.: Differential geometry, Lie groups, and symmetric spaces. London, New York: Academic Press 1978

    Google Scholar 

  12. de la Harpe, P., Karoubi, M.: Perturbations compactes des representations d'un groupe dans un espace de Hilbert. Bull. Soc. Math. France Mem.46, 41–65 (1976)

    Google Scholar 

  13. Hörmander, L.: Fourier integral operators. I. Acta Math.127, 79–183 (1971)

    Google Scholar 

  14. Hogreve, H., Potthoff, J., Schrader, R.: Classical limits for quantum particles in external Yang-Mills potentials. Commun. Math. Phys.91, 573–598 (1983)

    Google Scholar 

  15. Kostant, B.: Orbits, symplectic structures and representation theory. Proc. U.S.-Japan seminar in Differential Geometry, Kyoto (1965). Tokyo: Nippon Hyoronsha 1966

    Google Scholar 

  16. Kobayashi, S., Nomizu, K.: Foundations of differential geometry. Vol. I. New York: Interscience 1963

    Google Scholar 

  17. Kuwabara, R.: On spectra of the Laplacian on vector bundles. J. Math. Tokushima Univ.16, 1–23 (1982)

    Google Scholar 

  18. Montgomery, R.: Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations. Lett. Math. Phys.8, 59–67 (1984)

    Google Scholar 

  19. Sternberg, S.: Minimal coupling and the symplectic mechanics of a classical particle in the presence of a Yang-Mills field. Proc. Nat. Acad. Sci. USA74, 5253–5254 (1977)

    Google Scholar 

  20. Schnider, S., Sternberg, S.: Dimensional reduction from the infinitesimal point of view. Lett. Nuovo Cimento34, 459–463 (1982)

    Google Scholar 

  21. Schrader, R., Taylor, M.: Small ħ asymptotics for quantum partition functions associated to particles in external Yang-Mills potentials. Preprint

  22. Vilenkin, N.Ja.: Fonctions spéciales et théorie de la représentation des groupes. Paris: Dunod 1969

    Google Scholar 

  23. Weinstein, A.: Asymptotics of eigenvalue clusters for the Laplacian plus a potential. Duke Math. J.44, 883–892 (1977)

    Google Scholar 

  24. Weinstein, A.: A universal phase space for particles in Yang-Mills fields. Lett. Math. Phys.2, 417–420 (1978)

    Google Scholar 

  25. Weinstein, A.: Symplectic geometry. Bull. Am. Math. Soc.5, 1–13 (1981)

    Google Scholar 

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Guillemin, V., Uribe, A. Clustering theorems with twisted spectra. Math. Ann. 273, 479–506 (1986). https://doi.org/10.1007/BF01450735

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  • DOI: https://doi.org/10.1007/BF01450735

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