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Circular symmetry and the trace formula

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References

  • [A.M.] Abraham, R., Marsden, J.: Foundations of mechanics (2nd edition). Reading, Mass: The Benjamin Cummings Publ. Co. 1978

    Google Scholar 

  • [C1] Chazarain, J.: Formule de Poisson pour les variétés Riemanniennes. Invent. Math.24, 65–82 (1974)

    Google Scholar 

  • [C2] Chazarain, J.: Spectre d'un hamiltonien quantique et méchanique classique. Commun. Partial. Differ. Equations6, 595–644 (1980)

    Google Scholar 

  • [Co.1] Colin de Verdière, I.: Spectre du Laplacien et longueurs des géodésiques périodiques I. Compos. Math.27, 83–106 (1973)

    Google Scholar 

  • [Co.2] Colin de Verdière, I.: Spectre conjoint d'opérateurs pseudodifférentiels qui commutent I. Duke Math. J.46, 169–182 (1979)

    Google Scholar 

  • [Co.3] Colin de Verdière, I.: Sur le spectre des opérateurs elliptiques à bicaractéristiques toutes périodiques. Comment. Math. Helv.54, 508–522 (1979)

    Google Scholar 

  • [D] Duistermaat, J.: On the Morse index in variational calculus. Adv. Math.21, 173–195 (1976)

    Google Scholar 

  • [Do.1] Donnelly, H.: Spectrum and the fixed point set of isometries I. Math. Ann.224, 161–170 (1976)

    Google Scholar 

  • [Do.2] Donnelly, H.:G-spaces, the asymptotic splitting ofL 2 (M) into irreducibles. Math. Ann.273, 23–40 (1978)

    Google Scholar 

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

    Google Scholar 

  • [G] Guillemin, V.: Band asymptotics in two dimensions. Adv. Math.42, 248–282 (1981)

    Google Scholar 

  • [G.G.V] Gel'fand, I.M., Graev, M.I., Vilenkin, N.Ya.: Generalized functions, Vol. V, New York: Academic Press 1966

    Google Scholar 

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

    Google Scholar 

  • [G.U.1] Guillemin, V., Uribe, A.: Clustering theorems with twisted spectra. Math. Ann.273, 479–506 (1986)

    Google Scholar 

  • [G.U.2] Guillemin, V., Uribe, A.: The trace formula for vector bundles. Bull. Am. Math. Soc.15, 222–224 (1986)

    Google Scholar 

  • [G.U.3] Guillemin, V., Uribe, A.: Reduction, the trace formula, and semiclassical asymptotics. Proc. Natl. Acad. Sci. USA84, 7799–7801 (1987)

    Google Scholar 

  • [Gw] Gutzwiller, M.: Periodic orbits and classical quantization conditions. J. Math. Phys.12, 343–358 (1971)

    Google Scholar 

  • [H] Hörmander, L.: The analysis of linear partial differential operators, IV. Berlin-Heidelberg-New York: Springer 1985

    Google Scholar 

  • [H.R.1] Helffer, B., Robert, D.: Etude du spectre pour un operateur globalement elliptique dont le symbole de Weyl présente des symmetries I. Actions des groupes finis. Am. J. Math.106, 1199–1236 (1984)

    Google Scholar 

  • [H.R.2] Helffer, B., Robert, D.: Etude du spectre pour un operateur globalement elliptique dont le symbole de Weyl présente des symmetries: II. Actions des groupes de Lie compacts. Am. J. Math.108, 976–1000 (1986)

    Google Scholar 

  • [H.R.3] Helffer, B., Robert, D.: Comportement semiclassique du spectre des hamiltoniens quantiques elliptiques. Ann. Inst. FourierXXI, 169–223 (1981)

    Google Scholar 

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

    Google Scholar 

  • [W.1] Weinstein, A.: Asymptotics of eigenvalue clusters for the Laplacian plus a potential. Duke Math. J.44, 883–892 (1977)

    Google Scholar 

  • [W.2] Weinstein, A.: A universal phase space for particles in Yang-Mills fields. Lett. Math. Phys.2, 217–420 (1978)

    Google Scholar 

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Both authors were partially supported by grants from the National Science Foundation

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Guillemin, V., Uribe, A. Circular symmetry and the trace formula. Invent Math 96, 385–423 (1989). https://doi.org/10.1007/BF01393968

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