An algebra of pseudo-differential operators and quantum mechanics in phase space

A. Grossmann; Guy Loupias; Elias M. Stein

Annales de l'institut Fourier (1968)

  • Volume: 18, Issue: 2, page 343-368
  • ISSN: 0373-0956

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Grossmann, A., Loupias, Guy, and Stein, Elias M.. "An algebra of pseudo-differential operators and quantum mechanics in phase space." Annales de l'institut Fourier 18.2 (1968): 343-368. <http://eudml.org/doc/73966>.

@article{Grossmann1968,
author = {Grossmann, A., Loupias, Guy, Stein, Elias M.},
journal = {Annales de l'institut Fourier},
keywords = {functional analysis},
language = {eng},
number = {2},
pages = {343-368},
publisher = {Association des Annales de l'Institut Fourier},
title = {An algebra of pseudo-differential operators and quantum mechanics in phase space},
url = {http://eudml.org/doc/73966},
volume = {18},
year = {1968},
}

TY - JOUR
AU - Grossmann, A.
AU - Loupias, Guy
AU - Stein, Elias M.
TI - An algebra of pseudo-differential operators and quantum mechanics in phase space
JO - Annales de l'institut Fourier
PY - 1968
PB - Association des Annales de l'Institut Fourier
VL - 18
IS - 2
SP - 343
EP - 368
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/73966
ER -

References

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  1. [1] H. WEYL, " The theory of groups and quantum mechanics ", London, Methnen, (1931). Zbl58.1374.01
  2. E. C. G. SUDARSHAN, " Structure of Dynamical Theories ", Lectures in Theoretical Physics, Brandeis, 1961, (Benjamin). 
  3. [2] G. LOUPIAS and S. MIRACLE-SOLE, " C*-algèbres des systèmes canoniques : I ", Commun. Math. Phys., 2, 31-48 (1966). Zbl0144.23401MR34 #3357
  4. [3] J. J. KOHN and L. NIRENBERG, Commun. Pure and Appl. Math., 18, 269 (1965). Zbl0171.35101
  5. [4] D. KASTLER, Commun. Math. Phys., 1, 14 (1965). Zbl0137.45601
  6. [5] J. C. T. POOL, J. Math. Phys., 7, 66 (1966). Zbl0139.45903
  7. [6] J. E. MOYAL, Proc. Cambridge Phil. Soc., 45, 99 (1949). Zbl0031.33601
  8. [7] J. VON NEUMANN, Mathematische Annalen, 104, 570 (1931). 
  9. [8] V. BARGMANN, Commun. Pure and Appl. Math., 14, 187 (1961). Zbl0107.09102
  10. I. E. SEGAL, Illinois J. Math., 6, 500 (1962). Zbl0106.42804
  11. [9] R. SCHATTEN, Norm Ideal of completely continuous operators, (Van Nostrand), (1960). Zbl0090.09402MR22 #9878
  12. [10] I. E. SEGAL, Math. Scand., 13, 31 (1963). Zbl0208.39002
  13. [11] G. LOUPIAS and S. MIRACLE-SOLE, " C*-algèbres des systèmes canoniques: II ", Ann. I.H.P., VI, 1, 39 (1967). Zbl0168.23505MR37 #3823
  14. [12] T. F. JORDAN and E. C. G. SUDARSHAN, Review Mod. Phys., 33, 515 (1961). Zbl0118.44003
  15. [13] G. LOUPIAS, " Sur le formalisme de la convolution gauche ", Thesis, Marseille (1966). Zbl0132.09702
  16. [14] E. WIGNER, Phys. Rev., 40, 749 (1932). Zbl0004.38201JFM58.0948.07
  17. [15] L. COHEN, Journal of Math. Phys., 5, 781 (1966). 
  18. [16] L. HÖRMANDER, Commun. Pure and Appl. Math., 18, 501 (1965). Zbl0125.33401
  19. [17] A. ERDELYI, Asymptotic expansions, Dover Publications (1956). Zbl0070.29002MR17,1202c
  20. [18] D. IAGOLNITZER, S-Matrix and classical description of interactions. Preprint C.E.N. Saclay (France). Zbl0683.46054
  21. [19] G. MACKEY, Mathematical Foundations of Quantum Mechanics, Benjamin 1963. Zbl0114.44002

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