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Quantization of symplectic manifolds with conical points

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Literature Cited

  1. B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  2. A. A. Kirillov, Elements of the Theory of Representations [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  3. S.-S. Chern, Complex Manifolds [Russian translation], IL, Moscow (1961).

    Google Scholar 

  4. A. Borel and F. Hirzebruch, Am. J. Math.,81, 315 (1959).

    Google Scholar 

  5. R. V. Gamkrelidze, Izv. Akad. Nauk SSSR, Ser. Mat.,20, 685 (1956).

    Google Scholar 

  6. A. Weinstein, Lectures on Symplectic Manifolds, Amer. Math. Soc., Providence (1979), p. 48.

    Google Scholar 

  7. H. Hess, Lect. Notes Phys.,139, 1 (1981).

    Google Scholar 

  8. M. V. Karasev and V. P. Maslov, Dokl. Akad. Nauk SSSR,257, 33 (1981).

    Google Scholar 

  9. F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, and D. Sternheimer, Ann. Phys. (N. Y.)111, 61 (1978).

    Google Scholar 

  10. A. A. Kirillov, Usp. Mat. Nauk,31, 57 (1976).

    Google Scholar 

  11. F. A. Berezin, Funktsional. Analiz i Ego Prilozhen.,1, 1 (1967).

    Google Scholar 

  12. A. S. Mishchenko and A. T. Fomenko, Funktsional. Analiz i Ego Prilozhen.,12, 46 (1978).

    Google Scholar 

  13. J. Marsden and A. Weinstein, Rep. Math. Phys.,5, 121 (1974).

    Google Scholar 

  14. V. P. Maslov, Perturbation Theory and Asymptotic Methods [in Russian], MGU, Moscow (1965).

    Google Scholar 

  15. J. Czyz, Rep. Math. Phys.,15, 57 (1979).

    Google Scholar 

  16. M. V. Karasev, “Maslov's quantization conditions in higher cohomologies and analogs of the objects of Lie's theory for canonical fiber bundles of symplectic manifolds. I and II,” Moscow Institute of Electronic Engineering (1981), Deposited at VINITI, No. 1092-82 Dep. and No. 1093-82 Dep., p. 64.

  17. N. N. Nekhoroshev, Tr. MMO,26, 181 (1972).

    Google Scholar 

  18. V. Guillemin and S. Sternberg, Am. J. Math.,101, 915 (1979).

    Google Scholar 

  19. A. Weinstein, J. Diff. Geom.,9, 513 (1974).

    Google Scholar 

  20. L. Boutet de Monvel. and V. Guillemin, Ann. Math. Stud.,99, 161 (1981).

    Google Scholar 

  21. A. L. Besse, Manifolds all of whose Geodesics are Closed, Berlin (1978).

  22. A. Weinstein, Commun. Pure Appl. Math.,30, 149 (1977).

    Google Scholar 

  23. R. F. V. Anderson, J. Funct. Anal.,4, 240 (1969).

    Google Scholar 

  24. L. Hörmander, Commun. Pure Appl. Math.,32, 359 (1979).

    Google Scholar 

  25. M. V. Karasev, Exercises in Operator Methods [in Russian], Moscow Institute of Electronic Engineering, Moscow (1979).

    Google Scholar 

  26. M. V. Karasev, Dokl. Akad. Nauk SSSR,243, 15 (1978).

    Google Scholar 

  27. V. P. Maslov and V. E. Nazaikinskii, Izv. Akad. Nauk SSSR, Ser. Mat.,45, 1049 (1981).

    Google Scholar 

  28. M. V. Karasev and V. E. Nazaikinskii, Mat. Sb., 106, 183.

  29. V. P. Maslov, Zh. Vychisl. Mat. Mat. Fiz.,1, 113 (1961);1, 638 (1961).

    Google Scholar 

  30. V. I. Arnol'd, Funktsional, Analiz i Ego Prilozhen.,1, 1 (1967).

    Google Scholar 

  31. I. Satake, J. Math. Soc. Jpn.,9, 464 (1957).

    Google Scholar 

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Authors
  1. M. V. Kakrasev
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  2. V. P. Maslov
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Additional information

Moscow Institute of Electronic Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 53, No. 3, pp. 374–387, December, 1982.

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Kakrasev, M.V., Maslov, V.P. Quantization of symplectic manifolds with conical points. Theor Math Phys 53, 1186–1195 (1982). https://doi.org/10.1007/BF01027798

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