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References
R. Beals, A general calculus of pseudo-differential operators, Duke Math. J. 42(1975), 1–42.
F. Berezin, Wick and anti-Wick symbols, Mat. Sb. (1971), 576–610.
P. Cartier, Quantum Mechanical Commutation Relations and Theta Functions, Proc. Symp. Pure Math., v.IX, AMS, Providence, R.I., 1966, 361–383.
L. Corwin, Matrix coefficients of nilpotent Lie groups, Maryland Special Year in Harmonic Analysis, 1982–1983, Springer Lecture Notes, these proceedings.
C. Fefferman, The Uncertainty Principle, B.A.M.S. (new Series), v.9 (1983), 129–266.
S. Gelbart, Examples of Dual Reductive Pairs, Proc. Symp. Pure Math., v.XXXIII, AMS, Providence, R.I., 1979, 287–296.
A. Grossman, G. Loupias, and E.M. Stein, An algebra of pseudo-differential operators and quantum mechanics in phase space, Ann. Inst. Fourier (Grenoble), v.18(1969), 343–368.
L. Hörmander, The Weyl calculus of pseudo-differential operators, Comm. Pure and App. Math. 32(1979), 359–443.
R. Howe, On a connection between nilpotent groups and oscillatory integrals associated to singularities, Pac. J. Math. 73(1977), 329–364.
R. Howe, Quantum Mechanics and Partial Differential Equations, J. Fun. Anal. 38(1980).
R. Howe, A symbolic calculus for nilpotent groups, Conference on Operator Algebras and Group Representations, Neptun, Romania, Sept. 1980, Pitman Publishers, to appear.
A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk. 17(1972) no. 4(106), 57–110 (translated in Russian Math. Surveys 17(1962), no. 4, 53–104).
J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure and App. Math. 18(1965), 443–492.
J. Ludwig, Good ideals in the group algebra of a nilpotent group, Math. Zeits. 16(1978), 195–210.
G. Mackey, Unitary representations of group extensions, Acta Math. 99(1958), 265–311.
G. Metivier, Hypoellipticité analytique sur des groupes nilpotents de rang 2, Duke Math. J., v.47(1980), 195–221.
K. Miller, Parametrices for hypoelliptic operators on two-step nilpotent groups, Comm. P.D.E. 5(1980), 1153–1184.
D. Poguntke, Über das Synthese-Problem für nilpotente Liesche Gruppen, preprint.
L. Pukanszky, Lecons sur les représentations des groupes, Mon. de la. Soc. Math. de France, no. 2, Dunod, Paris, 1967.
L. Pukansky, On characters and the Plancherel formula of nilpotent groups, J. Fun. Anal. 1(1967), 255–280.
G. Ratcliff, A symbolic calculus for 3-step nilpotent Lie groups, Ph.D. thesis, Yale University, 1983.
R. Strichartz, Invariant pseudo-differential operators on a Lie group, Ann. Sc. Norm. Sup. Pisa, v.26(1972), 587–611.
H. Wevl, The Classical Groups, Princeton University Press, Princeton, N.Y., 1939.
N. Wildberger, Quantization and harmonic analysis on nilpotent Lie groups, Ph.D. thesis, Yale University, 1983.
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Howe, R., Ratcliff, G., Wildberger, N. (1984). Symbol mappings for certain nilpotent groups. In: Herb, R., Johnson, R., Lipsman, R., Rosenberg, J. (eds) Lie Group Representations III. Lecture Notes in Mathematics, vol 1077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072342
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DOI: https://doi.org/10.1007/BFb0072342
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